I really hope when you say "she did grumble once or twice about being sick of Bittybabyfast" that the she you mean was the birthday girl and not Grandma. Because while a an older sibling complaining about their younger sibling is completed understandable, Grandma complaining is not.
Oh, this is pretty constant for her - she makes little half-PA comments (usually after voluntarily spending time with the girls) about how they're running her ragged or how she's ready for a nap. She doesn't mean any of them, I think, but I really do try not to presume on her on the rare occasions I really did ask her to provide babysitting. So for the last six months or so, every time she says something about how she's overwhelmed, DH or I step in and take over and don't let her change her mind. She's doing it less often, now, so I think she's starting to learn that we're sick of having to guess whether her comments are just a ploy for sympathy, a real gripe, or just her being bored and wanting to say something.
You're being too nice. And Grandma is being a narcissistic brat.
My mother does this a lot as well. Her "martyrdom" mode will kick in and she'll start to say how Angel makes her SOOOO tired, and how she needs SOOO much rest after spending an hour or two with Angel. It's just a passive aggressive ploy to make you feel guilty about how much energy she's had to spend, and you're supposed to play your part by grovelling to her. Or fawn over her. Or tell her over and over again how GRATEFUL you are for her help.
She's not being nice. She's being helpful and playing Grandma when it suits her, and turning everything into herself. It's not about you, your DH, or your kids. She probably does love the kids but with a narcissist, it's almost always about herself - what a great grandma she is, what a great MIL she is, what a caring mother she is and how EXHAUSTED she is becoming by a GOOD person to everyone. In short, she's a martyr.
How I handle my mother? Just tell her, "Oh since Angel tired you out so much, I'll give you a break and not come over next week." Or "Oh, you're tired? I see. We'll go home now and give you your well deserved rest". If she's at our house, I'll hand her her bags, open the front door and say "I guess you better go home to rest. I'll see you next week". And then no matter how she protests, we go home, or I'll insist that she leaves. She's learned not to make such comments to me.
And about being helpful - I have learned that genuinely helpful and caring people do not try to forcefully help others and then use passive aggressive comments to force expressions of appreciation for their efforts. It took me a long, long time to learn the difference between true love and care, and drama-queen martyrdom love and care. I hope you learn to see the difference too.