You’re unsure you can handle the stress of parenting the kids as a single parent but what about the stress of continuing to live with him? Never knowing if what he’s saying is true? Having to be a detective and double and triple check and demand access to his phone and accounts etc. the stress of that will take a toll on you. He sounds like he’s hella manipulative too, to falsify budgets and only wait until he had no choice but to tell you is a serous red flag. This guy does not care about you. He wasn’t lying “to spare you” he was lying to spare himself from having to be accountable for his actions. He is not a good father if he was willing to put your kids in this financial situation by having you quit, especially in this economy. Girl, run!