I feel the same way that my child (soon to be children) is MY baby, not anyone else's. WTF - DH and I made him! I'm a lot more assertive about it now and couldn't care less if anyone else's feelings are hurt because it's totally normal to want to comfort your baby if he/she is crying etc.
But when DS was born, I began to feel unreasonable because of suggestions I was keeping him all to myself (we did visit relatives often and had visitors here) and felt neurotic for wanting to comfort him when he was crying in someone else's arms.
Looking back, I should have just smiled and said that he was MY baby, not everybody's baby as was suggested to me. It may have been down to mild PND but when MIL said DS was everybody's baby, I felt like he could be taken away from me and she and her family could do what they liked regardless of my feelings as his mum. The fact that they didn't give him back to me when I asked and did other stuff like feed him when I wasn't ready to wean him compounded that. What was I supposed to do - wrest him from their arms? No mother should have to ASK for her baby back.
It was a really horrible time for me and I probably over reacted but I was really upset about it all for a long time.
I also get upset hearing about other new mums experiencing similar sort of stuff especially when I know how giving birth, becoming a mother for the first time and all that can really rattle even the most secure and settled person.
LemonadeGirl, you're probably not as upset about it all as I was but if you're not happy about the way things are being handled, I'd put my foot down in the early days and nip things in the bud before it gets established.
That was an essay. Sorry.