Ok ... so the "he is not my BF" comment ... yeah .. truth dart her on that. Thing is she will make a stink that the kids are starting to wonder who the OM is ... not your circus not your monkeys on this one, tell W you are not going to lie and cover, (Her actions have consequences) if asked you will do the best as a parent you can do given the situation. Its tough with the kids and YOU have to figure out what the best age appropriate message will be ..... but I can almost bet the farm your W is lying to them and that will serve to wreck the R between her and the kids as it did mine (Something she is currently working HRD to fix)
I had the same issue ....Truth dart her.... "He is not my BF" my reply .. "OH? what shall I call a guy you are sleeping with then? Because last I knew 'friends don't %^#$" It seriously chapped me she exposed our S to OM ... still does and the A has been over for a bit and we are actually working through the garbage from it all.
As far as her noticing your GAL and mentioning how she is irked she is not a part of that ... yup. Not the life you asked for , she fired you ... you can validate there and slip in a "I would do alot of things differently" but just continue to live the life you have been given at this point.