I'm sure the children would love it if things were cool between you all. I know my dsd does.
Her mum used to really hate me, thought I was nothing to do with dsd and I was referred to as "fat tart" ROFL . You'd have though I had been the "other woman" but I wasn't.
But I kept my distance and did my best not to piss her off and eventually she warmed towards me. Took about 8 years though!
Now if I'm with dh when he collects dsd we go in for a cuppa, and when we dropped her off after last year's holiday we ended up having fish and chip supper there, and on dsd birthday we all went out for pizza.
I do think it's much better for dsd. You could tell at her birthday that she loved having all her family from both her mum's and her dad's around her. It's helped too when she has played either of us up because her mum can phone us and we can support her and vice versa. Dsd can no longer play us off against each other, and it's helped both her mum and us to know that if she is behaving badly then it's just her, rather than something here that's upsetting her or something at her mum's.
Things came to a bit of a head a year or so ago when dsd arrived for a visit with ALL her things in a suitcase - announcing that she was going to live with us. Because her mum felt so comfortable with us by that time we were all able to sit down and talk it through with dsd and sort things out. Her mum actually insisted that I was there.
It's helped as well because if dh is ill, too tired to drive (he drives a lot for his job and dsd lives some distance away) I can go and get dsd instead of him. Or in the school holidays when I am off work I go to get her during the day. There was a time when dsd's mum would have refused to let me do that, but now she doesn't mind it's helpful.
I do feel that if you can get on then it is helpful and good for the children. You are, after all, another significant adult in their lives. I think a relationship of some sort is probably something to be worked towards, but unless she is willing to make the effort too then there's probably not much you can do.