OP, have you ever met someone who 'talks' a good diet? There's loads about now, in January offices will be full of them - they will be going on 5:2 or Weight watchers, or MFP, or Forver living stuff, or low/no carbing, and you know you shouldn't have X because it does Y to your body, or it contains Z... and judge everything you eat loudly. Then by mid-to-end January, after hearing all this crap and being made to feel bad about what you've been eating, they'll stop being on a diet and be sat there stuffing down the cakes or chocolates someone has brought in, or have picked up a cheese ladened pasta for lunch etc.
Thing is, normally you'd not notice what they ate, if it was 'naughty' foods or not, but because they'd bent your ear about it, made you feel shit about your food choices, you find yourself judging their 'bad' food choices when they inevitably do give up the diet.
Your mum's done the same with your DD, you probably would just think "oh well, she doesn't really like playing with small children" if she'd not gone on about being a very involved mum or about how much she misses her DGD. It annoys you more because you've had to listen to her "talk a good grandmother".
Go out with her. Arrange things, she's not going to just play with DD in the house and you'll all get bored.