Hi Allgood
Firstly can I say I'm so sorry you are in this situation. It can't be easy to go through so much upheaval and I think you're coping really well
Secondly I think you have to decide what sort of single parent you want to be.
This is going to sound a bit harsh but I've seen this with so many of my friends and they (not you, my friends) fall into two camps:
1) the mothers (and it's all mothers, I don't know any single fathers whom I am close to) who are not yet prepared to fully let go. They want to punish their partner, will use every opportunity to needle their partner and will use subtle (and not so subtle) mind games on their children so the children perceive the mother in a 100% innocent light, the father in a 100% negative light and the new women as slightly more evil and deranged than Kim Jong Un.
The reason why so many of my lovely and rational friends do this is they want to punish their partner, are still in denial that they're single mums and want everyone to know that it's not their fault. Some people (because they love you) will go along with this because they hate to see you hurting or because they also feel the same way.
The problem with this approach is that its negative and hurts everyone. It hurts your ex-partner and his new partner (there is no reason you should care about this and I don't expect you too but it does reinforce his view that he is better out the relationship), it really hurts the children as the unit they've been brought up by and been told for so long is fun and loving has suddenly turned toxic and poisonous and that scares and unsettles them and assuming he has some access rights then you're telling them that every other weekend they're spending 48 hours living in the home of people they should hate. Lastly, it hurts you as one can't behave like that without some of the spite rubbing off on you.
2) the second approach is to be kind, magnanimous and accommodating (not a walk-over, but a human being and remind children to love and respect the adults in their lives whatever mistakes we make
I am NOT saying you are (1) or (2) but I AM saying that I have seen this so many times and EVERY friend of mine who has done (1) has spent a couple of years getting bitter and twisted.
(2) is the way to go but probably comes with a therapy bill (seriously) or some seriously good friends you can unload. Friends of mine who have done (2) have ended up happier and more stable and when YOU meet your next partner you've set a precedent.
I hope it all works out, you're well within your rights to go for (1) but (2) will make you and your children happier!
Hope this helps and GOOD LUCK!!!
XXXXX