Rant

Absolutely not, I used to do this when my cousins tried this, but if her kid is older make sure she doesn't hear cause it's not her fault and she shouldn't have to be sad bc of something her mom did, or you could always just tell your husband

Honestly, I can understand why you’re feeling fed up with it ❤️ If you’ve already tried to make an effort and every time you go you end up feeling pushed out and basically left to watch the kids while everyone else chats, I’d probably stop wanting to go too.
I actually don’t think it would be rude to still go and take your daughter to the park if that’s what you had agreed on. You’re not doing it to make a point or punish anyone, you just want to spend time with your daughter and actually enjoy the day rather than sitting around feeling awkward.
You could always just say, “That’s okay if you don’t fancy the park anymore, I’m still going to take [daughter] for a walk/play for a bit.” Then you’re not making it into an argument or expecting anyone to come with you.
And honestly, I think it’s okay to stop trying so hard with someone when you feel like you’re getting nothing back. You can still be friendly and make an effort, but you shouldn’t have to constantly fight to feel included. ❤️

Taking your child to the park is a legitimate activity that doesn't need to be sabotaged by an adult who cba. I'd leave them to their relationship if they don't include you and don't bother with the sister at all. Go where the love is xx