Hi i so understand how you are feeling x.
I remember when me and my ex split up just over a year ago, well i found out he had cheated on me and kicked him out same day. He went straight to hers. First weekend after, he came and took kiddies out on his own, aged 3 and 6, brought them home early cause he didn't know where else to go.
He then said he was taking them to his new house, thus meeting his new partner! i was distraught, all to soon etc but wanted him to see kids as ...well i don't actually know now what i was thinking, i was still shell shocked.
However they went and had a nice time, no dramas and said 'she' was nice. It hurt a bit, actually alot, tbh, i was hoping they wouldn't like her, even though i hadn't badmouthed her at all. I did feel that the kids were safer with two of them than just him as he isn't very practical etc.
The first of everything is defo the hardest, birthdays, Christmas, New years eve etc, you feel so resentful and just remember the good times, or imagine them times were good but in actual fact they weren't in my case!
I'd say whatever you do, try to keep things friendly, if the children seem to like her and have no complaints just grin and bear it for their sakes, you don't want them feeling guilty for liking her.
It does get easier however it will always niggle you!! Take care x