Hey, Immawildthing, I saw your first note come through about your MIL, and now this one, and I can really relate to what you are feeling. You feel threatened. It sounds like maybe you are worried about a loss of control, as well. I married at the very young age of 18, and had my first baby at 19. My husband and I lived on my in-law's property. My MIL was SUPER EXCITED to have a grandbaby. You can imagine how that went. When the baby was only a few days old, she came over and wanted to take the baby all around town to show to people. I, being very young and not having the wisdom or boldness to know how to handle the situation, let her do it but insisted on going along too. After that things got a bit better but I still felt very unsure of myself as a mother, and therefore threatened by my MIL's attention to my baby. Her confidence with the baby bothered me. Her familiarity bothered me. I just didn't feel comfortable.
Looking back, there was nothing really wrong that my mother-in-law was doing, except maybe not being sensitive enough to what I might be feeling as a new mother with a first baby. She was excited about the baby. I just didn't feel comfortable enough with her to relax about it, and I didn't know her well enough to be honest.
I know this is your second child, so you are probably a bit more confident as a new mother than I was, but your MIL is still very new to you, and obviously very excited about having a grandbaby. It's hard not to want to get into a power-struggle, I imagine. Just remember that you are this baby's mother, and she realizes that. She just wants to hold on for a little while.