Have you even been to court yet? Sounds like you haven't. If divorce is imminent, then you need to get an atty. and file NOW.
As for your ex 'dictating' what you can and cannot do in your home, she has no right or grounds. Only if it is court-ordered can it be dictated what you can or cannot do in your home. Regarding dating, unless you're associating with known pedophiles and the like, the court doesn't care whom you're with, as long as they do no harm to the child in any way.
She can threaten to get a lawyer, but they wouldn't even begin to be able to do anything until a petition for dissolution and custody is submitted to the court and an initial hearing is completed. One thing about threats: that's exactly what they are. You need to educate yourself on the Big, Wide World of Divorce and Custody......and coming here to this site is a great first step. Read everything you can get your hands on and get informed, or she will yank your chain as much as she wants. But unless she can put her money where her mouth is, all it is is hot air. By educating yourself, the next time she tries this, you will know whether she's just all blow or not. Remember: YOU ARE A PARENT TO THIS CHILD, TOO.
Read on this site and anything else you can get, get an atty., and file a petition for dissolution and custody. Document, document, document! Start a journal if you have to, but write everything down and keep track of everything you do, buy, or go regarding your child. Others here will have suggestions also, I'm sure.
You're at the beginning of a possibly long and (it sounds like) volatile ride. Hang on, keep the focus on your child, and maintain your cool around your ex at ALL times. And come back here often, if for nothing else but support.