I had a second interview with just the Principal and at the end he told me that the expected salary range was $35 an hour (I currently make $25). He was very open and I left happy with the salary. However, during my third and last interview with just the COO, I unexpectedly answered his question when he asked me what I was currently making. He continued saying that he was looking for someone who was motivated and willing to work hard and he's willing to pay $26, 27, 28 dollars an hour if he had to. I didn't say anything then but I left with mixed feelings. I am currently underpaid for what I do and I am looking for a position that would offer more. Should I mention that I know what the expected salary is? I don't really know how to go about it because I don't want to offend him but at the same time I don't want to get short handed (by the way, I am a female).
Numbers during the interview are just for discussion. What matters is what they offer you on paper. If you don't like the offer at that time, you have a ready-made argument of "the principal suggested I should be worth more than that" . But, as always, you need to decide what amount is acceptable and be willing to walk away if you don't get it, and they need to decide what you're worth to them and be willing to lose you if they can't afford you.
Personally, I hate this kind of dickering. But unless you like their first offer enough to take it immediately, negotiation is part of the process... and a verbal offer isn't worth the paper it's printed on. And you don't have offers, just handwaving where either or both of the interviewers might have been out of step with current policy or simply be evaluating how much they need you differently.
First, you need to decide what is the bottom you are willing to take or else you will walk away from the offer. If you already have a job, underpaid, then you might not be willing to move to another underpaid job, even if it is slightly higher.
You have the advantage of knowing a number from them, and they have an advantage of knowing what you are currently paid. However, what you are paid now really shouldn't matter: their pay scales don't depend on the pay scales of a different company.
First, go read some at AskAManager about negotiating salaries (such as http://www.askamanager.org/2015/04/ask-the-readers-tell-us-about-your-successful-salary-negotiations.html). Then, when you get to the offer stage, tell them at least a bit higher than your base limit. And as long as their offer is at or above your base, go ahead and take it. You do have to be willing to walk away if their offer is lower than your base. And occasionally, if your base offer is too high, they won't deal at all.
As someone else with low pay, one tactic I would use, providing I was willing to walk away from the offer is "You know what I'm paid now, but I'm also paid low. I'm not willing to leave this job for less than x, because why should I go to another job where I am underpaid?" Make sure you include some wording about how you do want this particular job too -- you need to want the job, have a lot to bring to the job, but not for less than x.
As a woman working in a male dominated field, I'll tell you that your gender isn't relevant to what they offered you, but it is relevant to how you responded to their question about what you're currently making. If a man had responded to the question about your current salary by just telling them the figure, the company would have also lowered their offer. It's in the company's interest to get the best possible candidate for the lowest salary. You fell into a trap that women (in general) fall into more easily than men (in general).
The short answer is wait for the written offer and make a rational decision about whether that salary works for you or not. The long answer is more my advice on how to prepare yourself for salary negotiations in general. The underlying reason that many folks are underpaid is because they don't negotiate well, and the good news is that it's something you can train yourself to do better even if you don't like doing it.
You have to practice negotiating because doing it well probably goes against your instincts. It's going to sound goofy, but I actually practiced out loud what I would say if asked questions around salary negotiations. I figured out ahead of time what salary I would accept and what effect "soft" benefits like working from home etc. would have on that number. I just can't do that on the fly because of my personality, and I know that the person extending me the offer wouldn't be doing their job well if they didn't get me to come on board for the lowest salary possible. You are the only person who will look out for your interests - other folks might be nice and help you when their interests don't conflict with yours, but you can't count on it.
If you feel that you're underpaid at your current position, then you might have said something like "My current salary is why I'm looking for better opportunities. I'm willing to start out at $35/hour and work my way up once I've demonstrated my skill." in response to the "What are you making now?" questions.
It's not too late to fix it though. Think about what you really think you're worth as an employee and ignore the previous numbers. Once you know what a fair offer looks like to you, tell them "This is what it will take for me to accept the job." Practice how you'll word it if you're going to do it face to face. If it's a written communication, ask a friend to look it over to make sure that you're being direct and not vague or wishy-washy. Think about all the different ways that someone could respond to what you're saying (even unlikely ones, like "you're crazy if you think we're going to pay that!"), and what you will say in response. You won't use 90% of that, but being prepared for anything will give you more confidence.
You have to overcome your tendency to suppress your first instinct because it might offend someone. Being direct about what you want isn't offensive as long as you're polite. On the contrary, it actually increases most folks' respect for you. It's not easy to change - I've worked on it for years. One thing that helped me was a self-defense class where we trained to recognize and overcome that urge to suppress our instinct to avoid a potentially dangerous situation because we didn't want to offend that scary looking guy in the dark stairwell. That's an extreme situation, but being able to recognize that feeling that you get when you're about to agree to something or do something you don't want to simply because someone might get offended if you refuse is a very important skill that impacts all parts of your life.
The "askamanager" link is something that you must definitely read.
If you don't think you are able to do hard negotiations with them, just tell them that you would like a written offer, but they should make an offer based on what they think you are worth, and not based on your current salary, and that you are happy to start if your numbers agree.
(That request asks them for exactly what they should offer you and not more; it admits that you made a tactical mistake by telling your old salary, but also demonstrates that you are not willing to work cheaply because of that mistake; being happy to start if your numbers agree means you are happy to walk away if they don't but without saying it. I wouldn't wait for the offer, because the written offer will be low if you don't act, and increasing a low written offer is very, very difficult).