Please read this as I'm offering some understanding which I think you'll appreciate.
I think it's a little mean to say the OP is BU. It's such a difficult relationship- the MIL- DIL one.
I get on fantastic with my MIL but when I was pregnant and just after I had the baby I really struggled and could not be around her. There are certain things that make a mum feel like a mum and it's hard enough making a MIL see that her son is now a father and DP and not just her little boy anymore, but there are serious boundaries to be set when it comes to your children.
It seems that MILs quite often like to act like the children are their own, want to spend time with just the child rather than you, their son and their grandchild, and like to have 'special time'. mums don't see why because it's their child, not their MILs child.
The best thing I did was just dropped my guard, stopped being so possessive with the baby, stopped taking everything she said to heart, and started giving her allocated time with the baby so that she can stop treading on my toes. I was being a little unreasonable before but in my opinion, MILs are unreasonable about babies.
Now I get on famously with my MIL and see her much more often as I appreciate her and like the break for an afternoon now and again when she minds the baby, and she's given up drinking to do so as I refuse to let anyone around the baby who has had a drink.
A little give and take on both sides is good and if you let her have some special time with the baby she'll stop trying to get in on yours.
But no, I don't think you're being unreasonable because being a mum brings certain attachments and feelings that you can't help.