I know how much it hurts to take on tons of responsibility, hoping for a leadership role that was, in fact, promised to you. You've made it clear that you did so many things including advancing your own money, either to show your dedication or to make them so grateful that they'd "promote" you, or both. But volunteers don't always have the commitment skills we would hope for, and non-profit groups don't always run like corporations. So the leader led you on, and you threw yourself into this entirely in order to get the payoff of troop leader, and then she made a decision based on her daughter's priorities.
But she has the same problem you do - a child (her daughter, your son) with other priorities/schedule. Maybe she remembers you have Cub Scouts, maybe she doesn't. (I have volunteered extensively and honestly don't know who has what on what nights - I'm too focused on my own stuff. But even if she did know your schedule, she's the leader, and she feels she has a responsibility to the troop as well as her daughter. Maybe she figures she can get plenty of other volunteers even if it doesn't work for you.
I am reading your SWH to mean that neither you nor your husband are willing or able to shed your Cub Scouts responsibilities. You are not willing to divide things up (one parent take Cubs, one take GS) or train someone to take your place. Are you both completely indispensable to Cub Scouts? Can you alternate attending the meetings and do the rest of your volunteering at home at other times? Is there no way to carpool with other parents in some way, even if it means families feed dinner to another family's kid and do the driving on alternate weeks?
If not, then look at the bigger picture. Isn't the purpose of Scouts to teach confidence, leadership skills and independence? Wouldn't it be beneficial in many ways for your daughter to shift to another troop and get to work with a new leader? (Alternatively, why couldn't your son switch to another Cub Scout group?) If you don't particularly admire this leader, maybe your daughter would truly benefit from understanding that someone broke a promise and made a decision that requires everyone else to adjust. Maybe she learns to deal with disappointment, and maybe she learns a lesson in keeping promises, because what one person does affects another person. Besides, kids get new teachers every year - they don't stay with the same one, nor do they stay with the same classmates. They learn to meet new people and find new advantages and great experiences.
I am dismayed that you even list the concern of having to run into this leader in the community! Really, is it that grave? If it is, please reevaluate your priorities vs. your daughter's feelings. It really sounds like this is having a much greater effect on you, because you've been cast aside and not valued no matter how much money and time you put in, vs. your daughter truly being broken hearted over the long term. So what you do is you hold your head high, trust that your volunteering efforts will be recognized and appreciated by people of good quality and integrity, and hope that your absence from the first troop leaves a really big hole. This will make it a huge learning experience for the "problem" troop leader. And you smile and say "everything's great" if you are asked. Mostly, you place the value of Girl Scouting above the whims of a few volunteers who don't always make good decisions.
It would also seem to me that you have the whole summer to possibly do what you wish she had done - find another meeting place that works for all, for example, or train some additional leaders/volunteers. Show yourself to be the leader you hoped they would recognize, but do it in a way that doesn't undermine anyone. If you let this devolve into pettiness or hurt feelings, or if you inadvertently add to the drama you feel someone else created, you'll wind up teaching your daughter the exact opposite of what you hope to gain from Scouting.