I really want her to come, but I dont want to come across as pursuing or anything like that. I want to make her feel that I am letting go.
You really want her to come. and yet... You want to make her feel that you are letting go.
Think about that.
You have incongruent thoughts swirling around in your head.
I'm sure your body language is just as confusing to her as well.
Go on the trip without her, tell the kids that it will be ok, you want to make her feel like you're "letting go", you actually have to start letting go, when your actions are congruent with your thoughts, then it's authentic, that's when it's believable because it's real.
Asking her to come on a trip and paying for her will be pursuing.
I know, it feels weird, it's counter intuitive but so far what you've been doing that you think doesn't feel as weird to you hasn't been working that great.
Don't be an a$$hole or a prick, just go on the trip without her.
Or better yet...
Leave the kids with her, go on the trip by yourself and have a real vacation, it's ok, you're allowed, you can be a little selfish sometimes without coming across as an a$$.
