Nothing wrong with buying a gift. Of course provided the gift isn’t something weird

It’s not the same as there was no abuse or infidelity, but my ex husband and I remain friends for life. But we are not alone in it. I know many other people who remain friends. I’d say if no children involved, perhaps it’s uncalled for but when there are kids, it’s good to stay on good terms (if possible, sadly you can’t be on good terms with some people, still you want to maintain civility).

It’s good for the kids and for others involved. For example you don’t want to make your kid’s wedding or graduation party guests uncomfortable because you and the father have obvious animosity. I’ve been to events like that. Very uncomfortable for all involved, especially one’s kids .

Remain appropriate and civil but continue moving on, that’s the plan!