OK, lots of stuff on my mind, none of which is coherent.
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8th day is somewhat based on science (though by “accident”.) Not until a week of age do infants make their own slnv84jnafof (maybe vitamin K?) that they need to stop bleeding, fend off infections, etc. This is why they get a K-shot in the hosp. (IIRC)
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While there is no hard and fast rule about when infants can/should be taken outside, there are some considerations. Infants have a more difficult time fending off/recovering from virus, colds, etc. Therefore, Mrs. Spritle were recommended not to take The Littlest Doper out in crowded, confined spaces for 3 months. Now, this is not a rule! Mitigating circumstances include cold/flue season (definately an issue for TLD), duration of excursion, number of people, size of area, and, (most important) decision of parents! We took TLD out long before the 3 months out of necessity.
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Both of my boys have been brissed (?). I’m a non-practising non-denominational nothing and Mrs. S is a somewhat practising Jew (is Jewish, follows most holidays, goes to temple most every Saturday [drives there], doesn’t keep kosher, hasn’t read hebrew since her bat mitzva, etc.) Mrs. S wants them raised Jewish and I didn’t care. My/our goal was simply to raise them to be moral, compassionate individuals with a strong sense of self. I didn’t care if they got this from Judaism or Buddhism for that matter.
This is merely to say that my situation is a bit different from yours so what I say is useless to you. 
However, my two sons and two nephews were all brissed by the same mohel. At my second son’s bris, one of the nephews (not brissed by Rabbi Malka) felt a bit out of place (he’s 4 yo.) A consideration in the decision to bris/not bris (regardless of circumcision decision) is Aaron’s sense of self. Might he feel out of place when with cousins, etc.? (if applicable) I know that all my nephews and my son (the younger is too young) love looking at pictures and people, and the bris pictures are something that they like looking at. (not to say that you should consider the bris because it’s a good photo op.)
Anyway, I’m rambling. I just wanted to give you some considerations.
to sum:
Bris when/if you want, after day 7 of life.
Taking a baby into potential germ situations is not as safe as not doing so.
Aaron’s sense of self may be affected in some way by your decision to bris/not bris.
Now for my unrequested opinion:
Assuming the decision is to have him circumcised (and it sounds like it is) get him circumcised by a mohel. They are trained to do this procedure and do many a week, every week, every year. Hospitals use residents/doctors who may do 2 each week. The methods used by the two are different.
Interview the mohel. Find out what instrument/procedure he uses. Find out what anesthetic he uses (if any.) My nephew was brissed Sunday and the mohel proudly stated that the only anesthesia used was good old sugar water – as had been done for thousands of years. I was sickened and wanted to yell, “They didn’t have lidocaine 2000 years ago!”
You can have Aaron circumcised by a mohel without it being a bris. (Rabbi Malka has done many snippings on the goyim.)
As far as the MIL thing goes, take a stand. Take a firm stand.
Mrs. S and I have one rule of parenting: Pick your battles; stick to your battles; fight them to the death. To back down is to allow MIL to stick her foot in the door.
Best of luck and welcome to Aaron. (and lots of nachas to the parents.)