Wow! this is the first time in 5 years I am not automatically siding with DIL
that said YANBU to be irritated by MIL - as is shown on mumsnet regularly it can be very fraught with an annoying doting MIL and a baby particularly PFB.
YABU to not cut her a bit of slack. It is quite simply a question of different eras/parenting advice.
When I had DC1 years ago you could start to wean at 4 months, now it's six. Sleeping positions is another - Back To Sleep was excellent for reducing SIDS but not new research/trends make such huge differences. I used infacol for DC1 - now wouldn't for DC2 as some research has shown it has little effect at all. Cod liver oil used to be used rather than vit D supplements etc etc
I know it is a case of wanting to be heard and respected and it sounds instead like a battle of wills/control freakery but face it, you are going to cause huge family tension by allowing your mum to have him 2 days and your MIL not at all.
Bottom line- she has brought up a baby really well - must have done as you fell in love with him.
She will provide TLC that can be got from a childminder yes, but not all childminders are equal.
The rusks - i get it, i do - my MIL wanted to give dippy eggs early but we had allergies in the family so I wanted to wait, but looking back I was being pfb about it, certainly in how abrupt/dismissive I was rather than seeing it for what it was which was echoing little things she had done with and for DH, ditto baby powder, ditto wanting to give a bottle...
I exclusively bf and extended bf and boy did I lord that over her in retrospectshe used to like to watch but that was the only way she could feel connected with the milk as I refused to entertain the idea of mixed feeding or expressing nipple confusion etc but again I was a bit petty about it
The hand mitts is hilarious - I know what she means though 
I often thought DD looked cramp even though knew she was fine - but really you have said you are not cutting the nails as often as you should and that's not her fault - don't blame you either, hate cutting nails but that's by the by
The medicine would depend entirely if it has to be taken every feed or a specific time or if it is proven to be an essential/has conclusive benefits rather than a placebo/give it a try prescription. I could talk at length about overprescribing and the baby industry but as I do not know the details I will try and butt out.
Pram outside - many advocate a bit of cold freah air - particularly Scandinavia and quite a few nurseries might also do. Sleeping in pram outside if baby not at sitting up stage etc not worst thing I have ever heard - it would help promote sleep. If can be seen from window or heard from monitor would not be unduly concerned unless there are neighbours with big dogs or totally exposed area or rough as fuck area (not being a snob, have lived in areas where I wouldn't leave my cat out let alone a baby and others where I would feel perfectly safe doing so. The media and internet have made a great deal out of baby snatching and paedophiles etc and many children have lost out as a result)
So...you will probably have less resentment if you make other arrangements but you are going to have more rows with DH and MIL as a result of that decision.
Rusks - would not kill me
Free hands - would not kill me - Would ask MIL to cut nails as 'her' job
Meds - would not kill me, would give later - unless absolutely critical
Air outside - would not kill me but would request back if front dangerous
But I say that now as a mum of two with third due in a few weeks and without support from family (MIL cancer, mum away) so I cannot be anything other than biased.
Am aware that with my pfb nothing my MIL did was seen as anything other than oppressive, controlling, competitive and interfering. I rejected all of it. It is only now I see she just wanted to be let in, included, have her opinions respected if not followed and be allowed the freedom to dote on her first grandchild 