You need living arrangements that can accommodate visitation with all those kids and a place with a pool that the kids will WANT to visit, then as the more responsible more loving parent you just do your job, pay your modest support and be the best parent you can be until such time that you can petition the court for primary custody of your children. Based upon their ages, they will have a lot of say in which parent they choose to live with and your wife just doesn't really care about them at all right now as she destroys their security, their family AND their father.
Get on some men's rights websites. You've got to be really prepared and document everything for a number of months, even years to eventually "beat" her at this game but your youngest is 8 so really you only have 10 years at most left.
Your wife is a entitled terrorist you can't negotiate with or ever trust so there is no bargain or deal to ever be had with her. This is one situation where I think cutting her off financially, letting the house go, improving YOUR situation to the best of your ability and protecting yourself (and your kids) is priority number one. If your wife hits rock bottom in the process and "repents" so be it. Get out of God's way. If she wants to "save the house" ....let her get a job. She can work now while you have visitation.
Do you have 50/50 visitation?
The internet is 90% complaining and entitlement and I hate it because I deserve better!
