Every marriage is different. In mine: my husband wouldn't be staying out at hotel or anyone else's house for the night. I wouldn't even think of doing that, I wouldn't be okay with him doing that.
Your husband sounds like he doesn't care or respect you enough to be planning nights with his ex, he's a liar and if he didn't cheat yet (gone through with it), sounds like he will eventually. It's up to you to either get divorce or be his doormat while he emails other women, lies and disrespects you. Good luck to you, hoping things work out and you can find peace