Apologizing can appear to a WAS as pursuing. There is no problem apologizing, just do it once, for any specific issue, and then let it go. Don't expect a response from your W. If you DO get one, sit with it and do not respond at this time. Your reason to apologize is not a tactic to open dialogue, it is to apologize. Period.
Good that you are working on your relationships with yourself, your children, and God. Keep doing those things. Life gets better and these are positive growth.
What is the intention you have with OW? Is she truly just a friend or is she someone you would consider or are considering a romantic involvement with? If she really is just a friend, someone to go for coffee with and that you would not put preference over going with her or going with another friend, then so be it. If it's simply to have female company, fair enough.
The reason I bring this up is, if you are interested in trying to R with your ex, the consequences would be the hurt that might cause this lady. How clear are you, regarding your intentions with your lady friend?
I think it was good for you to bring up Disney to your W, although her response was "typical". She doesn't trust you. Even her response to your request for forgiveness could be construed as "normal" behaviour.
Of course she wants you to feel better. So she could very well just be telling you she forgave you, in order for you to feel better and move on. In the mean time, she still doesn't trust you (if trust was one of her issues, then she hasn't completely forgiven you), so she comments on how you only asked her as an afterthought.
What I am putting out there is, if you wanted to invite her, simply invite her. Let her know it's an open invitation. It will be up to her to decide if she is going to go, or not, for what ever reasons she has.
I do want to also point out though, that it is interesting that she indicated that if you take the kids, it would hurt her MORE than anything else you have done, yet she won't go with you (at this time).
