Sounds like a combination of things to me.
1) She feels overwhelmed by more than one child at a time.
2) She is more comfortable with little boys than little girls.
I know #2 seems odd, since after all, she is a girl herself, but it can be true. I know when I was pregnant with our 2nd child, I wanted a girl, but was a little scared since I was so "familiar" with little boys. I would have been happy with another son, since I felt like I knew what I was doing with boys at that point (my son was almost 3, lol). A daughter? That was a scary unknown quantity. I know, it's dumb. Every kid is different. Blah blah blah. But it could be her mindset as well... she doesn't know what to "do" with girls.
Maybe you could arrange for a girls day and the THREE of you go do something fun. I'm not into hair and nails, but if your MIL is, then do that. Or go have brunch or tea and cookies somewhere.
Is your daughter involved in any activities? You said MIL doesn't ask about her... maybe she doesn't know what to ask. Does your daughter do dance, or tap, or gymnastics, karate, equestrian, swimming.... does she love reading books and trips to the library? What does she DO? Invite your MIL.
For the longest time, my daughter didn't "do" much. She just was dragged along with older brother to his stuff. Then she got old enough to have her own things... and she does more than he does these days. And it isn't all "typical" girl stuff, like gymnastics or dance classes. Maybe your MIL doesn't know enough about your daughter's activities to ask much. If she is familiar with Football and Tball and basketball... maybe she doesn't know that girls play soccer and basketball and volleyball, too.
There could also be a small bit of the puzzle in that she is judgmental about there being a 3rd child, especially if she knows that you didn't purposefully plan to have a 3rd. It may be subconscious.
So... try to "help" her by offering information leading into a conversation about or with your daughter, when you can. And make sure you aren't doing the opposite, which is talking only about your daughter so that she has to interrupt you to ask about your boys. Talk about all of your kids, don't go overboard the other way.
And the biggest thing of all: remember that your kids will get their self esteem from their accomplishments and their work/effort, and how you respond to the same. A person not in the core nuclear family will have way less influence. And eventually the kids will see any inequities for what they are-- a problem the grandma (or whomever) has. I know my kids learned that about some of our extended family. They don't take anything personally... just see it as the weirdo person we are related to and their issues.. not ours.