I would get on and do some research about how the family courts work and the types of evidence required if you want to show why it's beneficial to have anything other than a 50/50 residency arrangement or any restrictions in place to cover possible abuse or child abduction, etc. There is loads on the internet about this, as long as you choose your sources carefully.
If you can avoid the courts, it is better. The whole process is stressful for all concerned and very costly. It also ups the ante and can encourage antagonism rather than co-operation. However, if you have a partner with abusive tendencies, it is as well to be prepared for taking things to court even if you try to avoid it. The simple act of knowing your facts and being prepared means you have an advantage and can't be bullied into anything.
If he's rubbish with the DC, the threats of running off with them are probably idle ones. It's seems to be part of a script that such men use as a way of trying to get their Xs to tow the line. The reality is that he probably won't want the responsibility. However, make a record of when he said it, and the context, on your computer. In fact, make a record of dates, times, place and comments every single time he says or does something that you feel is remotely abusive. It may well have a bearing on your case if it does go to court.
My guess is that if you stand your ground on this, refusing to become either upset or angry but rigidly calm but firm, he'll back down. Be prepared for things to get worse before they get better though.
Sadly, you may find that he has very little to do with your DC once the dust settles and he no longer sees them as a way of controlling you. Although that will hurt, don't chase after him as your DC will be better off in the end if their expectations aren't raised unrealistically high.
WHatever you do, do not allow contact to take place in your home. Not only is this a bad idea for enforcing boundaries around the end of your relationship with each other, it is confusing for the children.
Good luck with it all.