You have multiple problems happening here which need to be addressed separately. First you are significantly younger than the people who report to you and younger than people in professional positions are in general. Second, you are an experienced developer but not an experienced leader. Third, your subordinates are remote. Fourth, you may be perceived as looking down on them because they weren't high school programming prodigies (Note I said you may be perceived that way, not that you actually do. But in all honestly people tend to be intimidated by people who achieve something that is as far out of the norm as that is.) And fifth, the perception may be the opposite as well, that they will look down on you for your lack of formal education even more than for your age.
Dealing with being significantly younger
For the younger issue, this is likely to be a problem for at least the next ten years, so best learn to deal with it now. The key is twofold. First present yourself as professionally as possible. Use correct English grammar in your emails, don't make jokes that your high school peers would get, but which would not be funny to adults. While it is not applicable here due to the remoteness, dress professionally in meetings especially if clients are involved. People will have trouble taking you seriously, so you need to cultivate a serious demeanor. Let people know what experience you have in a matter of fact way. They will look at you and think, "He's so young" and you can't avoid that, but you want them to think next, "but he really knows his stuff."
The second part is to understand where they are coming from. Spend some time learning to understand the cultural history of the people you supervise. My sister likes to point out that different generations are alien to each other because they grew up in very different cultures. It is actually easier for the older ones to understand the younger culture as they at least saw it develop (not that the older people seem to do any better at this task).
For you it is harder because what is their culture is history to you (and if you supervised me, ancient history at that!) It might be useful to you to talk to people of the same age as your subordinates and get an idea where people of that age are coming from. Or read books/articles on cultural history if they are available for the age groups you are supervising. This link may be useful: http://www.beloit.edu/mindset/
Understanding what people of different age groups value and what their work expectations are will help you in knowing how to deal with them. But while are all exposed to the culture of our youth and it, to some extent, shapes our world view, we are also individuals and thus may not actually follow the norms (as you do not follow the norms of your own generation since most of them are not managing subordinates at your age), so talk to them individually and find out what their expectations of you are and what they expect of the workplace. Interns are tricky because (even though they are older than you) they are relatively new to the workplace and often have unrealistic assumptions about how things work. But to help them get rid of those assumptions, you need to talk to them and find out what they are.
Dealing with being an inexperienced leader
First you need to realize that getting them to do the work is your first priority. Yes sure you can probably do it faster yourself, but it is no longer good enough for you to do the work, you must teach them and mentor them so that they can do the work. You will need to delegate and given that you started work so young, you are probably good at what you do and it will be very hard to let go. Do not do their work for them. Do not fix their mistakes, but return them to them to fix. (How else will they learn?) Do not be a snob about how they do things. Ask them to fix incorrect work, yes, but when there are multiple ways to do something, do not insist that your way is the only way.
Treat everyone with respect. Listen more than you talk. But don't be a pushover either. Management techniques that work fine when everyone is a dedicated employee with a lot of skill fall apart completely when you have a problem employee. Since you seem pretty self-motivated, it may be hard for you to realize that many people need to be supervised more closely or they won't produce much or do anything more than adequate work.
And sometimes they have personal problems that affect work. Likely you haven't run into that much yet, but people get divorced, they have deaths in the family, they have drug or alcohol problems, they have personality problems that make them hard to work with. You have to learn to deal with things on a professional level while still showing some concern about their personal lives, it is a hard line to straddle sometimes. Keep your focus on performance and cut some slack when a really big problem occurs. Be prepared to rearrange the workload if a someone goes to the hospital or loses a family member.
It may have seemed intrusive when you were not managing people , but managers need to know the status daily of everyone's assigned tasks. Are they on time, are they behind, are they stuck on something they can't figure out. Are there roadblocks that are keeping them from finishing something,. It is now your job to remove those roadblocks as much as possible.
Remember it is a whole lot easier to be more restrictive at first and then ease off as they prove themselves, than to start off giving them lots of freedom and having to rein them in later because they couldn't handle it. Now I'm not saying to micromanage, but you will need to make sure they know what company standards to follow and what they need to do in relation to things like timekeeping and how much daily communication you expect from them and what you expect in terms of knowing progress. Don't let them flounder around for weeks and then have to come down on them hard because they haven't done anything.
Make sure to treat everyone well whether you like them or not. You are here to work with them not be best friends. The better you treat people the easier they are to deal with.
Dealing with remote subordinates
Communication is the hardest part of being remote. You need to set communication standards for them from the start. How accessible will they be? How often do they need to touch base with you? How will you deal with the person who never responds to emails, phone calls and IMs. Is he really working or not? If at all possible meet these people in person. We have a lot of remote workers and if we bring them to the office for a couple of weeks, we seem to build better relationships with them. They are more likely to contact people they know, they will be more relaxed around you once they see what your personality and work habits are.
Dealing with the perception that you are looking down on them
If you treat people with respect, listen to their ideas and actually change your mind if they sell you on a particular point, you will be most of the way towards convincing them that you are not a snob who thinks everyone who didn't start programming at 8 is an idiot.
Another good technique for getting people to humanize you is to admit to mistakes. Sometimes when I am dealing with someone who is junior to me and he makes a common mistake or is embarrassed that he didn't see something, I point out a time when I made a similar mistake. I sometimes point out that the reason I know how to fix something is because I broke something in the past. You are less intimidating when you let people know you don't think you are perfect.
Try to learn from them too. They may very well have learned some things in their college education that you haven't learned yet from practical experience. I have found that even people I don't much like or respect have often had things to teach me.
Dealing with the perception that they are looking down on you
It is possible that they will look down on you because they have more extensive education than you do. It is hard for someone with a Master's degree to work for someone who hasn't graduated from high school yet. Be sensitive to this. But call them on it they treat you with disrespect. Make sure your own boss will support you if they try to go around you when they don't like a decision you made. Nothing ruins credibility faster than a first-line manager that the people above him won't support.
You may have to rein in some of their more abstract notions too. You are in the practical world of deliverables and deadlines and maintaining the product. Some of them might still be in the pie in the sky theory world. You may have to help them come down to earth with practical questions about how long things will take and whether the client will pay for a solution at that level, etc.
If possible having someone much more senior in the company introduce you to them can help as well. When they understand how much respect people in your company have for your skills, it will make them less inclined to think you are someone they can ignore or discount.
