Dude, I empathise with your plight. I think it's something that most male parents (myself included) have been through. It feels horrible… the loss of control, the crossing of boundaries which feel so crucial to maintain , the feeling of betrayal by your partner if she sides with an opinion outside the family unit which you are trying hard to build. Throw in a lack of sleep, the fact your world is upside down and your going up a steep learning curve with parenthood and it's a heady mix.
It's a bummer, but the fact is, it's a continuum. Just like water evaporates to form clouds which fall as rain, like the moon pulls on tide, like night follows day, mother in law's will express an opinion, which at a very basic level wives will want to respond to.
Your wife tolerates it without saying anything because her mothers opinion, like it or not, will carry a lot of sway at a very basic human level. It might go on forever, but now is not the time to worry about that. Most likely outcome is that in 6 months time, things will have moved on. You and your wife will have more confidence, be better rested, your daughter will be dishing out smiles which will lighten up your life. What your going through is hard, but it gets a lot easier, and quickly.
Your not over reacting, I remember pulling into a lay-by on the way to work and repeatedly punching the steering wheel to try to vent some anger at my parents in law's inference. But the fact is, there is nothing you can do about it, so vent on this forum, feel murderous thoughts when your out riding, and put up with the shit like every other male parent ;-)