I'm going to piss off half of mn here and just say go easy on him for now.
Don't take him with you to your mum's, give him some time and space for both of you to think and consider the situation.
Don't ignore his suicide threat, especially if he's had depression before and you're having financial difficulties. If he's not mentioned suicide before, then take it very seriously.
You need to set boundaries for both yourself, and for him. If you love him, and think he's a good person who's having problems at the moment, and not dealing with them in a good way, then tell him that. Tell him you still love him, but he needs to sort himself out and be a good husband and father, and if he needs outside help to do that, then that's ok, it's not a sign of weakness, and you will support him.
If you think he's a waster who's stringing you along and manipulating you for an easy life, then go with your gut.
Boundaries that you put in place are there to protect all of you. And if he's wanting to make a positive change, then he will need to understand that.
I know you have a lot on your plate, and in many ways this is the last thing you need, but it may be he's struggling more than you think, and needs your support.
All of my advice is based on my relationship with DH, in which we've both been depressed, we've both resented the other for thinking they've got the easier time of it, and both misinterpreted just how close to collapse the other one was.
DH responded to my first suicide threat with "you'll never do it", "you're just doing this for sympathy" "you're just doing this to manipulate me into feeling guilty" and within 3 days I was standing at a suicide spot ready to jump.
I know after the last 24 hours the last thing you want to do is give him any slack, but maybe he really needs you, and is just absolutely shit at asking for help, our even accepting it when it's offered.
I hope things get better for you all.