I know I'm going against what everyone else is saying here but I agree with you suiledonn.
It may very well be unreasonable but a lot of what you think at this stage usually is.
I am not very happy about my MIL babysitting at her house, only because my DD is a difficult sleeper at times and I know MIL just relents and takes her into bed as I fully understand that at 4am it's quite tiring trying to settle a baby but once she has done it we have about a week of trying to get her back to sleeping all night.
I'm sure it was the travel cot as she wasn't used to it. MIL has since got second hand cot with second hand mattress. What a fight we had to get her to allow us to buy new mattress.
My other main concern is that MIL smokes heavily, not in the house when DD is around. But I object to the co-sleeping because of this.
Anyway, the point I wanted to make is that we had to relent and allow DD to stay over. But we try to get MIL to our house as much as possible, so if its an early night to cinema etc then MIL comes to ours, and if we have wedding etc then DD stays at MILs.
What we have started doing also, as like you I had/have seperation anxiety (for want of a better phrase), is visiting for dinner, letting MIL bath and feed DD and settle her, then we sit for another hour or so having adult time and head home. we then pick up DD around midday, this is all more so to allow me to get used to leaving DD and also makes MIL think that the time is special and not just getting used for babysitting.
I hope this helps slightly? And good luck coming up with happy compromise