I agree that the real issue seems to be not the belief of your claims, but that your mom just doesn't seem to care to find out if they're the truth or not, and doesn't seem to care to get to know your DD to find out. She just seems to prefer the other Gkids, correct? To the point of talking about them incessantly and saying nothing about your dd?
My MIL would do that about niece. Niece was 10 months older than our DS, and they babysat for her part of each week, and thus were around her a LOT. Whenever ILs came to visit, it wasn't very long before they were going on and on about Niece this and Niece that. Often when we visited ILs and Niece, SIL and BIL were there, MIL would STILL spend more time with Niece and dote on her. When DS was about 9 months old, we took a car trip with ILs to visit relatives. Goodness, I got SO sick of hearing about Niece! I mean, it was everything, right down to her pooping habits! I mean, they were actually WITH their other grandchild for a long amount of time, finally, and it was like they couldn't even take the time to enjoy him and get to know HIM for who he was, without going on about Niece. The final straw during the trip was when we went shopping and went into a kids store. MIL immediately headed for the girls section and couldn't stop talking about buying something for Niece, with not a word for or thought about DS, who was right there! I was livid. MIL did offer to get DS something, but I think it was after I got very quiet and she maybe realized that she was ignoring DS. And the thing she offered to get him was exactly what she got Niece, and it was impractical for DS and his age and development level, which further cemented it in my mind that she was just so wrapped up in Niece that she couldn't see or appreciate DS for who HE was.
We did talk to them about the favoritism, and of course they denied it. And then MIL went overboard trying to make it seem like there was no favoritism, but it was so transparent.
None of this was helped by SIL, who seemed to have entitlement issues with her parents' time. OP, do your sisters seem to think that they have dibs on your mom's attention because their kids are older? And could that be why your sisters don't say anything about your DD's accomplishments? Or does your mom seem to act like this at all?
In my situation, it got worse before it got better. What helped me at least get my frustration out was to write MIL a letter and I laid it all out. I never mailed or gave her the letter, but when I would get frustrated, I would go back and read the letter to myself. Sometimes I would add some things to it. One of the lines I remember that I 'said' to my MIL was that I wanted her to get to know DS for the great kid he was, and not just as a poor substitute for niece when she wasn't there, because that's all it seemed he was when she constantly talked about niece in our presence. (Once again, I never actually did say this to MIL; it was only in the letter I never sent.)
I sort of like what WillyNilly said about about calling your mom out on it. BUT, I think you have to do it in such a way so that you don't come off as jealous. Because then your mom will just dismiss your concerns anyway.
One thing that worked for me: my MIL had a habit of inviting SIL and their family whenever we were doing something with them. It was annoying b/c I just wanted my kids to spend some time with their grandparents without the other grandkids(who got to see them way more frequently). Finally, I'd had enough and told her, "Oh, that's OK. We can just stay here if you'd rather go to dinner with SIL. We'll go with you another time." I kind of called her bluff and let her know very politely that I wasn't going to go if SIL was there. (MIL called SIL and uninvited her.) But could you do something like that? Make conversation about your DD and see how your mom responds. If she makes conversation about and engages with your DD, great. But if she talks about your sisters and their kids, don't respond, and then redirect her back to LK or other topics. Do that a certain number of times (like 3 strikes and you're out), and then if she does it again, get up and start leaving. If your mother questions it, tell her that it seems that she seems preoccupied with sisters and their kids, so you'll just come back another time when she can spend some quality time with LK. Be cheery about it, like you're doing both her and LK a favor. "It's not fair to LK to have her time with you interrupted by stories about her cousins when you're obviously missing them, and she's growing so much lately and is learning so many new things that I think it would just be better for you to spend time with her when you can give her your full attention."
If she balks, just remind her that you've listened to this, that and the other thing from her, yet all she's said is that LK is small. Be prepared to have her get huffy and accuse you of not wanting to hear about your sisters' kids. And you can always point out that you did hear about them, but that's not why you came to see her; you came to see her to give her some time to enjoy LK and she dosn't sem to be doing that. You could also point out that you're a relatively new mom, LK is YOUR child, you're proud of her and you love her, and you want others, especially her grandmother, to be proud of her and want to talk about her too. And it's no fun when LK is right there and she can't seem to enjoy her b/c she's so wrapped up in the other grandkids.
Sorry that was so long. I remember this so well and it strikes a nerve with me. (Oh, and DS is now a young teen and I have a MUCH better relationship with my MIL. It did take several years though. But my kids do things that SIL's kids don't, and MIL really seems to enjoy them now, for who THEY are.)