One: This one is pretty cut and dry for me, and I have some personal experience with it. I know my husband likes to take me out and sort of "show me off" to his friends. I am more introverted than him, so most of the time I would really prefer to sit at home and play with the kids or watch Netflix, but I made a decision to defer to him and trust his judgement so if he decides he wants me to go out with him, I'm going to go out with him. I understand that it can be difficult to find a sitter, but something being difficult is not an excuse. Expand your own social group. Make friends with other moms and take turns watching kids. My husband and I do not have family locally, but we don't ever have trouble finding someone to watch our kids. On the rare occasion that I can't find a sitter and there's no way I can take the kids along, my husband understands because he knows "I don't have someone to watch the kids" isn't my usual go-to excuse and he knows I have exhausted every option available to me.
Two: Something about this just doesn't add up to me. Isn't it going to look strange to his other coworkers that he's going solo to the wedding when they're all bringing someone? Wouldn't the fact that she tried to break you and him up be even more of a reason why he should want to bring you? Does she think she was successful? Part of a red pill lifestyle is having a Captain whose judgement you can trust and feel comfortable deferring to even if you don't necessarily agree with his decisions. The whole thing sounds fishy to me.
Three: I have dealt with female friends and family members who give both me and my husband grief over how we choose to structure our relationship. Their opinions are worthless as long as our relationship works and we're happy. He's confident enough not to let it get to him, and the fact that it doesn't get to him means it doesn't get to me. Again, it sounds fishy to me that he would exclude you from functions that welcome partners/spouses in favor of another woman's comfort level-- especially when that person seems to be opposed to his relationship with you.