Number 1: Lock your doors. You may be in a safe neighborhood or had some other reason for it to be ok (I grew up without needing to lock our door unless no one was home) but if you were already worried about what your mother might do, yeah... time to start locking.
Number 2: Chances are that she saw you running out to intercept him and sneak him in. That in itself looks guilty. Greeting him at the door as a friend would definitly have been the better way to go.
ok, sorry for the "hindsight" stuff, but had to point that out for future reference.
I'm glad that you are ablt to admit and accept that your mom was and currently is trying to continue her abusive behavior. That is a great beginning, and keeping that in mind can help you deal with her in the future. Next step is to talk to your kids. I don't recall seeing how old they were, but tell them the age appropriate truth, without the more personal details. "He (bf) is a very close friend and your mother (nana) does not understand or like the relationship. It may be best not to discuss it with her (nana) because it will only upset her." Nothing false there. And that if they have any questions, just ask you and you will sit and talk to them about it.
As for your mother. I have not had to deal with mine (as my own relationship ended before it became an issue) but I think the best route is to treat this like any other decision you may have made in your adult life. Tell her, in as much detail as you are comfortable with, about your relationship and that her approval is not required nor requested. If she will not under any circumstances accept that you are an adult making adult decisions with the consent of your DH and with the welfare of your children in mind, then yes, it is ok to tell her it is none of her business and to butt out.
Good luck and I hope others have better, hopefully firsthand advice for you.
Life is about the journey and not the destination,
so what better way to know life
than to wander all the roads and paths set before you.