Chestnut tree. You have my sympathy. Unless you have been there I think it is difficult to understand how hard it is, emotionally, practically and financially to be dumped by a partner and left to bring up small children alone.
Its also not all that helpful to have other posters with axes to grind based on their own personal experiences, wading in, at a time when what you really need is support and a safe space to vent your understandable anger.
The most helpful advice I can offer (have been there myself) is to focus on the things you can control. You might not like your ex introducing his new GF, but as long as he is not abusive, you do have to trust him with your child.
Get a schedule in place, then hold him to it. Take the time that you are on your own to recharge and to do other stuff. The first few weekends are awful, but it does get easier.
Do you have a financial settlement in place? If not get a solicitor and make sure that it is fair.
When you are at home alone, invite girlfriends over, get them each to bring something and all have a good gossip.
If you can afford it, get a counsellor, give yourself a safe space to vent and work through your feelings. I did this for the first 6 months and it made a real difference and helped me cope through that really hard first year.
For what its worth I would reccomend this book Leaving Him Behind: Cutting the Cord and Breaking Free After the Marriage Ends by Sandra S. Kahn
It was probably the most useful thing I read when my ex left me and it helped me establish the groundrules to build a new life for myself.
You can build a new life and it will get better 