I’d not be in a relationship with someone who lives with their spouse/partner (she can call him ex but what makes him ex? Not having sex? Ton of people are a couple but don’t have sex).

I’d demand she officially ends it by not cohabitating,, has a divorce decree and custody court order and is fully single.

No I’d not be FaceTiming with her kids either, sure they are asking. Kids always ask who is this and who is that.

Her inviting you over when “ex” (I use that term loosely here) is at work is fishy to me

None of it sounds like relationship material at all.