"I told her that her opinion did not matter..."
Hmmm.. I think any discussion with another person that includes the above phrase, should be reconsidered. This is your mother in law, you are living with her -- you may not agree with her opinion, but she should feel that her ideas and concerns are heard, acknowledged and that they in fact do matter.
I personally think 4 is young for a sleepover, and I think you MIL's anxiety has some basis. But regardless of the pros and cons of sleepovers for preschoolers -- there seems to be a tone in your post that I think is problematic when dealing with family members (since it benefits you to have a relationship with them on some level)
You state that you told her "she has no business knowing all of our friends", and " I just told her to mind her own " -- these are such dismissive ways of dealing with another human being -- that I can't help but think you would all fare better (particularly since you are living together) if you approached her with a bit more regard.
I'm not saying you have to cave in to her every whim -- but I think if you acknowledge that you hear her concerns, and then reassure her and try to assuage her anxieties (in this case by telling her how well you know the family, and how comfortable/confident you feel with them) you might all feel better. Taking the tact of telling you MIL to just butt out -- seems ill advised, especially when you are guests in her house.
It is not unreasonable that she would feel anxious to hear that her 4 year old granddaughter will be spending the night with people she has never met. Perhaps if you brought her with to drop off to meet them, she would feel better. Perhaps not -- as I don't know how well you actually know these people or how debilitating your daughter's allergies are (you say they are raging right now?)
But whatever the situation, and whether you actually convince your MIL (or me) of your point of view or not, the bottom line is that I think it helps to try and reduce anxieties in others by reassuring them, not by simply dismissing and attacking them. Especially when it comes to complicated relationships like MIL's.
In any event -- given the dynamic between you and your MIL -- I say good luck getting through the next four months!