Therapy - and probably just for you. And talk about what you want to do, and where you see yourself and your marriage in 5 years, 10 years, 20.
If being apart is in the cards, then do so. If being together is, then go all in. This in-between stuff is what's tearing you apart.
Oh, and another thing. For the love of God, please don't say you're staying together because of the kids. Because all you're doing is teaching them a loveless marriage is their lot in life if they have children. You have thrown an enormous responsibility on them for your future -- and they're not even in fourth grade.
At least own up to it, that you're staying together because of, well, what, exactly? Money? Inertia? Fear of losing your reputation? Something else? Because if there's nothing keeping you together other than a vague "it's for the kids" sentiment then, news flash, there is nothing
keeping you together.
Will your children be better off if your marriage ends? Why yes, they will! See: https://www.psychologytoday.com/us/blog/when-kids-call-the-shots/201703/why-bad-marriages-are-worse-kids-divorce
And like I said above, if you're going to continue your marriage, then jump into the deep end and work on it.
FYI because your wife stinks at money management, no matter what happens with your marriage, please open up trusts for your children with someone in charge of them who is neither you nor your wife until your children turn 18 (you might want to ask the lawyer who would set up the trusts). Why am I suggesting this? Because your kids could stand to have their credit and futures not destroyed if Mom 'forgets' to pay the bills (no, your kids' credit ratings aren't affected if the house goes into repo unless they're listed as part-owners. But I've got enough friends whose parents were dirt broke when they - my friends - left the nest, and it can be an enormous hump to get over. One friend is out of college for over 35 years and she is still paying her student loans).
Check tax implications as you may find this is better than an inheritance. And, when they turn 18, they can use the $$ as they wish, whether it's to put a down payment on college or a house, get married, or just bum around Europe for a year. It doesn't even have to be a lot. Putting away $50/month for your eldest child gets them $7200 + interest by the time they turn 18.
Note: I am not an accountant or a doctor, and I am not your lawyer. All I'm trying to do is give you a nudge. But it's up to you which direction that goes to.