L.,
Some people have been unnecessarily brutal to you. I hope that won't stop you from listening to the kinder and thoughtful people on this site.
You are learning how to be a good Mom (as all of us have to do) but under difficult circumstances. I don't think your wanting to be alone with your boyfriend as making you a bad Mom. You are certainly entitled! Different people do things differently.
As complicated as it is for you imagine how hard the whole thing is to understand for a 3 year old who is developing.
Things I would consider.
1) Until you are in a committed relationship you may not want your child to meet any boyfriend you have. Then I think it would be appropriate for your son to go to Mamaw's when you go out on a date, but I would make overnights very rare. And I would limit dates to once or twice a week. Avoid confusing your baby by not even allowing them to meet until the relationship reaches a certain level.
2)Maybe you are in a committed relationship? If you and the "boyfriend" have discussed it and think that you may end up marrying then yes I would have your son involved to see if you are comfortable with how your boyfriend is with your son. But take it slowly. Be sure to spend quality time alone with your child to avoid jealousy but if you were married Mommy and Daddy would go out on a date occasionally. Mommy and boyfriend should be able to do that too.
3)If you are at #2 and your child does well with your boyfriend when you are out of the room, then spend more time in the kitchen preparing dinner. Go have to make a few phone calls. Don't leave them totally alone but give them more space. Eventually maybe you can be on the computer in the same room but allowing them to interact, play a game, build some leggos. Eventually I bet your baby will gain comfort.
Good Luck!
p.s. You and the boyfriend might consider a parenting class together too! That might help the boyfriend feel he knows what to do and give you confidence too.