Are people actually reading what the OP is writing? She keeps reiterating that the GPs have had her DD for a few hours on their own on several occasions. That's not the issue.
OP, trust your instincts. Psychologically, it is not good for a child of that age to be away from their mother for long stretches (more than a few hours). She is too young developmentally for it to foster independence, etc. Being away from you for too long will make her more clingy, not make her less so. Psychologically, it would be worrying for a child of 18 months to be fine with being away from his or her mother for a whole day or night (would indicate a weak bond). She is as independent as she already is precisely because you keep her appropriately close and she knows that Mummy is always there to come back to quickly if she feels overwhelmed or whatever. As you are a bit AP (as am I), you know this makes sense and flows with the rest of your parenting style.
You don't have to say yes. She is your child, you do you think is best for her. Personally, if my DM was bahving this way, I'd tell her in no uncertain terms that the more she pushes at this issue, the more she makes me adamant that it's not going to happen.
Frankly, I think she is bloody lucky you let her see DD as much as you do, if she's treating you that badly. It's fine and probably normal for Grans to think you should be doing things how they did, but not to go on and on saying hurtful and offensive things like your DM is doing. Has she actually offered a reasonable, logical and well-thought-through explanation as to why it'd be much better for your child to be without either of her parents for whole days or nights?! Of course not, she's just parroting the out-of-date and illogical stuff she was told as a mother back in the day and also using it an excuse to get to relive those days via your DD. Well, your child is not a toy or a time-machine!
Tell her that you don't feel secure letting her have your DD for so long when she is so critical of your parenting and are liable to do stuff that will confuse DD or undo the good work you put in. Tell her that when she starts respecting your parenting style and your rights as a capable adult to parent how you like then you will consider it more seriously. If she has anything about her, she'll quit the nitpicking and put-downs and realise she needs to STFU. She can't expect to talk down to you and try to undermine you that way and then expect the 'reward' of DD. You need to set new, firmer boundaries with her for your own self and to ensure that these crappy patterns don't trickle down to DD, when older.She had her time to parent how she wanted, now it's yours. You sound a great mum, btw :)