If a person is the least bit annoying, judgmental, hard to be around for whatever reason, that person should not, in any circumstance, be in the delivery room.
Labor will go much smoother without any added stressors.
My mother stopped by during my first labor, sat herself down with her knitting needles and regaled me with tales of her 3-4 hour labors and mentioned that I must be doing something wrong to be entering into my sixth hour. When she left for dinner, I told the nurses not to let her back in --- voila! problem solved and I was able to have the relaxing birth experience I desired. For the second child, we alerted no one that I was in labor, so there was no issue with pop-ins (also helps that I tend to give birth in the wee hours of the morning).
As far as out-of-town guests... if the person is the least bit annoying, or feels like they are the guest, they do not need to stay over in the first month or so. If the visitors are willing to take on the role of housekeeper, personal chef and grocery shopper/errand runner --- fabulous. They still don't need to stay in the house, but a local motel would be fine. If, however, they will be a drain on finances, emotions, feel like they can insert opinions on baby's eating/sleeping/pooping habits -- they shouldn't be allowed in the door for the first month. Breastfeeding/no sleep/ bleeding / exhaustion / pain & soreness / living in a night gown.... do not make for good house guest entertainment.
I had a houseguest stop by when my second baby was 6 weeks old. She expected to hold the baby non stop and didn't offer help with chores. That was semi-ok because I was back on my feet and able to cook/clean. It would NOT HAVE BEEN OK in that first week or three.
That first week home is brutal, surreal, etc. The biggest help is to have someone come and DROP OFF meals, hot meals even better; tell you that you look fabulous, and then quickly leave.
Good luck! Be strong against the MIL.