Your MIL sounds awful because I also have a MIL who will NOT take no for an answer and keeps on asking and asking and asking and asking, hoping one of us will cave and give her a different answer.
She also lies and will say she will do/won't do something and then does what she wants anyhow, ignoring the wishes of the parent (seen it many times with her looking after SIL's kids).
She thinks she knows best and won't listen.
OP doesn't think physical affection is bad, she doesn't want adults kissing her baby on the mouth. I was advised the same by my Dr, as it is how whooping cough and herpes/coldsore virus are easily transmitted - which can be lethal to babies. Among many other diseases and viruses.
OP and her DH have made the best decision for childcare for THEIR family. Not to suit MIL.
The thing with nursery is that if a carer gets sick, the child can still go. If the carer goes on holiday, the child can still go. If the carer and parent disagree or argue, the child can still go. The carers will listen to the parents requests and follow them even if they personally disagree. Sounds like her MIL would hold it over them.
They already visit at least once a month. There is no need or requirement for OP to have had her MIL look after her 6 month old baby yet, so why are people saying she is awful for not giving any babysitting to MIL. Maybe she doesn't want to leave her baby and maybe just not with MIL.
My MIL will/has never looked after my children. She isn't what I consider capable. She doesn't listen. She only wanted to when they were small to take them and show off to her friends about them. Not to actually look after them as she showed no interest at all if we visited unless other people were there.
Not everyone has nice helpful MIL's. Some MIL's want to help but actually just want to take over, ignore boundaries and be right, be the most important, be the best, be first etc.