He does support and defend me but feels sorry for my mil as she's been through alot
It's quite common, unfortunately, for people who have had very difficult childhoods to become narcissistic and controlling when they are older. Your MIL's behaviour really fits the bill here.
The only thing people like this respond to is uncomfortably firm boundary-setting. By this I mean you have to be prepared to put your foot down HARD and not give in when the inevitable tears and cries of being victimised start.
So the first time she comes to snatch the baby away, you physically turn away and say clearly, "Sorry, I'm still holding her. You (or BIL etc) can have a cuddle in a few minutes." Hold out for a period of time and then let her have the baby. If she comes over complaining, just be firm. "No, sorry, I'm still enjoying MY cuddle. You can have her soon." She has to be absolutely clear that your word is law and YOU are in control. Repeat this constantly. You have to establish yourself as the boss. If she is smart, she will understand what is going on here.
If she starts carrying on and complaining, you have to be prepared to set a harder boundary and be utterly clear about the behaviour you will NOT allow. "MIL, every time you come over, you snatch the baby away from me repeatedly and won't give her back. I don't like it being kept from my own child so this needs to stop. If you continue trying to take and keep my child from me when I want her, we will reduce contact."
Narcissists fear abandonment, so although she will likely go into a sulk to try to manipulate you into backing down, you have to show her that you are made of stronger stuff than she is. She will eventually come crawling back and although she will probably make passive-aggressive remarks about it, you can ignore these as weak protests.
You cannot let her walk all over you, as she absolutely will if you let her.
Most people are capable of understanding other people's boundaries and of respecting them without even being asked to do so. Narcissists cannot and will not, so unfortunately it's on you to make a show of dominance that they can understand.