Good advice from fedupbutfine. Just focus on getting yourself good, solid and clear advice, and take no notice of your ex's empty threats.
Yes, Im sure he is 'serious' about his threats as of course his new lady love will be sublimely happy with a voluntarily unemployed DP complete with his children in tow, the best part being she has to support them all..oh joy 
As for his hissy fit..oh dear..all's not well with him, is it? A new life with his new love to look forward to, yet he's still yapping on to you about you driving him to his affair, etc. A foot in both camps, methinks. Well, tough. Let him pour his heart out to his new lady, and stop making your ears available for his bullshit. Honestly, there's no point why would you even want to waste time listening to all that?
Screen him out and focus on your priority, which is to get all the advice you need. My ExH was always threatening to take our 2 DCs from me (all you are now is a 'single mum'). Nothing ever materialised beyond a lot of talk, it didn't take long for me to put a stop to that. I'd a life to live and it didnt include taking time out to listen to him spout nonsense on an ongoing basis.