I don't want you to get angry with me and of course I don't know your MIL so this is just my take on what I've read. Why was it a big deal that your MIL wanted to hold the baby? She's his Grandma.
I think in order to have a healthy relationship sometimes we need to think of what's irritating you about the person and ask yourself, Is this something I should be angry about or is this something that isn't a huge deal? Again I'm just going by what I read, I'm not there so this is a very distant observation.
I was a bit older when I had my kids, 35 when I had my Son, 36 when I had my Daughter. My in law's weren't young. But they never stopped over and when we wanted them to see the kid's we'd have to bring all of our stuff there. They loved the kid's but I could tell when it was time to leave. I thank God my Mom was around as much as she was. I was exhausted and she'd watch them when I worked part time. My in laws weren't really comfortable babysitting. I could have them watch them for a couple of hours but that's about it.
My Father in law passed away 5 year's ago he was 80 something. My MIL is 81 now and she spends a lot of time with the kid's now. I wish they had gotten to know their grandfather better, but they were young and he was older.
I have learned that if someone just stops by they get what they get, messy house, me with bad hair and maybe not ready for the day. It is what it is, we are who we are. I have never had anyone complain, I don't stress about it.
I'm not saying you're wrong and their right, I'm just saying next time you're frustrated with them take a step back and a deep breath and ask yourself if there really is a reason to stress or get angry.
Only one I'm frustrated with is my MIL. I love my FIL. It's not that she wants to hold my baby, it's that she tried to go around me to do it. Its not that she wants to take my kids, it's that I don't trust her. It's that she acts like they're hers and I have no say in the matter. It's that she's always breathing down my neck, or leaning over my shoulder. She's a gossip and I don't trust her to keep any of my family's secrets. I don't trust her to let me be mom.
Just yesterday, the only reason she didn't give me crap about not allowing her to hold the baby, was because he was asleep. I honestly would have let her hold him yesterday though, if he weren't. Yesterday, the only problem I had was that she didn't ask to hold him, she hinted that she wanted him by holding out her arms like I was just going to hand him over; like she doesn't have to ask, I should just know she wants him and I have no choice but to give her what she wants because "she's grandma" and apparently grandmas come before mothers.
I actually pointed out that I noticed her hint dropping, to my husband, and he actually said, "I know, it bugs me too. Maybe next time, don't acknowledge her until she actually asks. It shouldn't bug her too much, if she catches on fast enough". So there was a little bit of support from my hubby, thank goodness.