1) Do document and stick to the facts, as it's been suggested.
2) Ignore stonewall's advice. If you assume an adverserial relationship, that's what you're going to get and as you said earlier, having a problem with a same sex couple is not going to help you with your potential coaching career. Turning a potential problem into a supporter will.
If she's determined to be adversarial, let her hang herself. Just document what goes on for future reference.
3) You should do everything possible to get along with her. Along these lines
a) When you next see her, tell her your apology was sincere and that you're thrilled that you two will be "working together". Use that phrase. Do not say she will be "helping" you and do not call her an "Assistant Coach" You do not want to say anything that could be perceived as diminishing her. Instead, you want to raise her status (and document that fact) in relation to you. You may even want to write something in advance and memorize it (and document it) beforehand.
b) If she has suggestions, let your 2nd Asst Coach respond to them before you do. If the 2nd Asst doesn't respond, prompt them by asking "What do you think?". If the 2nd isn't there, say "Sounds great. Why don't you see what xxxxx thinks"
Let the other Asst Coach be the one who complains about this woman. And if she complains about you, her complaint will be that you're cooperating with the lesbian mother. Her complaints will be a twofer for you (ie the lesbian mother will get complaints, and you will be portrayed as being cooperating with the lesbian mother which will inoculate you against potential future complaints that you're hostile to homosexuals)