Counselling? Really?!
I can see exactly where you’re coming from OP, and agree that you should just go by yourselves first, or just kind of go along with the idea, but avoid firming up plans. Or just explain you’d planned to go by yourselves the first time, so that’s what you’d like to do.
My MIL is absolutely lovely and we get along really well, BUT she sounds very similar to yours, in that she would take the baby out of my arms without asking at any opportunity. With my first child I found this very hard to deal with, it made me feel very uncomfortable, and very irritated. I remember one incident where I was breastfeeding (something I had lots of problems with and found quite difficult) and my DS scratched himself quite badly and started screaming. My MIL shot over and tried to take him out of my arms to console him, as though I, his own mother could not do it. On that occasion I stood firm and wouldn’t let go of him, but instead asked her to get me a tissue to wipe away the blood.
Having said that I know my MIL means no harm and just gets over excited and wants to spend time with her grandchildren, which is lovely. She is so hands on and it has been a Godsend having someone so willing and able to help with childcare. Plus DS (now 2) absolutely adores her. So I just bite my tongue! I’ve had another baby during lockdown and although we’ve formed a support bubble with PIL we haven’t seen them nearly as much as we normally would, and it’s actually been a relief to be able to enjoy the first few months with the baby, rather than feel like my baby is being taken away from me. I also find it hard because my own mother never tries to take my children out of my arms without asking, or push me out of the way to grab hold of the pram.
I do wonder whether any of the posters who are saying YABU have ever been in that position themselves. Imagine someone taking anything from you without asking, or pushing you out of the way so they can take over. If this happened with an inanimate object such as a drink or something you’d likely be shocked and annoyed, however imagine how it feels when it is your child! Of course OP isn’t being unreasonable not to want to spend a day feeling like that, particularly one that they wanted to experience as a family.
I never thought I would feel so annoyed/upset in that type of situation, but when faced with it, it is difficult to deal with, particularly when you’re trying to adjust to motherhood yourself!
Also, I do find mumsnet rather odd sometimes, as most of the time it’s all ‘just say no!’, and ‘don’t ever do things you don’t want to, just to please others’, yet for some reason when you’ve asked for advice you’ve been told you should just grin and bear it. Perhaps some of the other posters are MILs and can only see it from the other perspective?
YANBU!