You have yourself and 3 children to think of and worry about supporting...a total of 4 people. I would take 4/5 of the money out of your accounts. Leave him 1/5. That seems fair. At the moment, he is thinking about himself, so leave him enough money to take care of only himself.
I would call an attorney first thing Monday morning. See what your options are as far as the house, changing the locks etc. Maybe you would be legally protected if you changed the locks, even if his name is on the deed too based on the situation, and you taking the kids on an already-planned vacation. Having someone stay at the house to "guard" it isn't going to do any good. It's his house. If he can get in, he will. That's why the advice of an attorney is needed, to see what loophole changing the locks will fall in to, in order to protect your things. I'd also check into freezing whatever other assets you may hold jointly so that he can't clean them out...I mean things such as CDs, retirement savings, 401Ks. I'd also check with the lawyer about jointly held credit cards...perhaps there is a way to notify the credit card compnay that as of such-and-such a date, you are separated and is there a way to note that so that charges made by him after that date are not your reponsibility. If not, ask if there's a way you can pay it off and cancel it, and if there is, then do so. Get a credit card in your name (or maybe your and your Dad's name) only so you start to build a credit score of oyur own, that is not attached to his.
As far as hiring a PI...what for? I hate to be blunt, but it sounds like he is no longer invested in the marriage. Do you need a PI to tell you what you pretty much already know? He may say there is not someone else...when a 40 year old man leaves his wife and 3 children in an instant, there is someone else. Unless an attorney advises you that if you have proof that he was cheating that it could benefit you later, then it's money I wouldn't spend right now. I'd take the vacation...you and the kids need it. If you don't want to spend a lot of time with his side of the family, tell them why. A simple "I am sure that you understand, based on our current circumstances, why I'd prefer not to see you guys while we are here" will suffice. You haven't done anything wrong, so don't act like you did.
Watch the "I'll do anything to keep the marriage together" stuff. Tell him that you are more than willing to work to see if you two can save this marriage, but everything has its limits. Then decide your limits, and stick to them. Let's not have this guy thinking he's Joe Stud, with a babe on the side and a wife who's willing to tolerate the crap.
Counselling...get it for you and the kids, even when he tells you he doesn't want or need to go. It will be helpful.
Make him take responsibility for his behavior. If the kids ask you questions, make them ask him. Make him look at his 3 children and explain to them why he is uprooting and upheaving their entire existence. I wouldn't speak badly about him, but I wouldn't give him a pass either. If they ask "Why did Daddy do this?" say "I don't know. You'll have to ask him when you talk to him. But remember that Mommy loves you very much and isn't going anywhere". They will need the reassurance that one of their parents is stable and in the picture...it looks like it is going to have to be you.
I wish you well. Your next few months will be difficult, but empowering in many ways. Stay strong for yourself and your children, provide a positive role model for them, and as much stability as you can offer them during this unstable period.