This is indeed an unfortunate situation. Something doesn't feel right here. This is NOT a trivial mistake to make and you had verbal confirmation from HR, manager and director that this is indeed remote. One person screwing up is entirely possible, three people screwing up the same way is rather strange. 

Your best shot is to call the manager and/or director and talk to them. Be polite & friendly but also firm.

 1. State that you have negotiated in good faith, and that 3 persons you talked to you had confirmed that this is a remote position. If remote is mentioned in the offer, add this to the list. 
 2. Ask what specifically what has changed between yesterday and today. Why can this work no longer can be done remotely as discussed?
 3. State that commute is impossible for you for personal reasons.
 4. State that you have already suffered damages since you have quit your existing job based on their offer.
 5. Ask and/or suggest alternatives. What exactly are the aspects of the job that can't be done remotely? Are there any tools or processes that can help? How about coming into the office once a week? Can the role be modified to enable remote work? What other suggestions or ideas do they have?

You will have to take your cues from how the conversation goes. If this really was an honest mistake, they would be apologetic and will probably be open to at least exploring potential solutions. If they dig in their heels or are defensive/aggressive, than there is not a lot you can do. They may have intentionally misled and you don't want to work for this type of people anyway. Just tell them "I can only work remotely" and leave it at that.

Contact your previous employers immediately and explore if you can rescind your resignation. You may have to eat some humble pie in the process, but many employers are ok with that and will take you back without too much fuzz. Fire up your network and start looking for alternatives. You may not need them, but now is the time to get started.

> So here I am feeling confused, disappointed, mistrusting, and hurt.

You have every right to feel this way, but try to ignore this for now. You need to play this as professionally and level-headed as possible and strong emotions don't help