Unless you live somewhere that proof positive of infidelity will get you a meaningfully different divorce settlement, in which case ignore everything I'm about to say and go right the fuck ahead, I don't think you'll really gain anything from trying to get more evidence. All you'll do is further invite the risk that he'll catch you and decide that you deserve to be punished for not trusting him, at which point you and your children will be in even more danger than you already are.

You already know that he's abusing you. That should be enough to know you need to leave. If you can't bring yourself to do it for your own sake (though that should suffice! you matter! your happiness and safety have value!), do it for the sake of the children in your care who will otherwise learn the incredibly dangerous lesson that this is the way marriage is supposed to be. Every day you stay, you're not just hurting yourself; you're hurting them, too.