He's eroded your confidence so much that you think you can'd do anything for yourself.
Good news though, at least you are home, and will be able to get by, get help and support.
Don't think about why he has chosen to go AWOL, it's irrelevant, it's not even about you. It's HIM. His failures, his insecurities and his problem.
You have 'lost' a cheating, insulting and abusing partner. he is thousands of miles away and you won't have to share your DC with him. Yes caring for DC 7 days a week is tough, but you can handle it, millions of people do, and with more kids. You are just scared and uncertain of the future.
OK so none of us know how tomorrow will go, but let me tell you that one way or another, you will get through all this, and each day that you are not under his control, is another day that you will heal, grow stronger and begin to regain the confidence you lost.
Please keep posting, please keep asking questions when you are confused about things and your feelings, you will work it all out.
Stop chasing this prick. The sooner you move on, and get through this birth and new born stuff, you will start to feel stronger, and you will be able to move yourself onwards. The longer you cling to undesirable rubbish in your life, the more harm it does you.
WRT your DC and telling them anything. You don't have to tell them. You can just say that you don't know. Whatever it is, it's nothing you did, nothing the DC did, so it must be his issues. You have tried to contact him, and he isn't contactable. He knows where you are if he wants to talk.
This is not really that big an issue in your life, not really. It might seem that way, but it's actually all fear and all in your head.
You said yourself that he has never supported you, so no change there. You have said that he's always been a git. No change there. No loss to this rubbish. One day you will heal well enough to be an even stronger person than you were before you met him, one day you may meet the person you truly and richly deserve. But not when you have this deadweight in your heart. Cut him loose.