How are they feckless ? They know their daughter is financially secure, they've raised her, loved her and don't appear to have put her under any pressure to support them. They appear to have coped with the punishment of being disinherited without bitterness. They didn't need to save for the next generation as it had already been done at their expense. GGM could easily have left all to her own children whilst ensuring financial security for the next generation. She choose to play games with them. She appears not to have trusted her own child to look out for her children but trusted a baby ?
The OP, through nothing that she has done, is financially secure and in position of power over her parents. Yes, she wants to prioritise her future and that of her daughter but her mother wasn't afforded that luxury but was instead punished. A.teenager was punished by her family with that punishment passing down through the generations. Her daughter could potentially continue that punishment or could do the right thing and ensure that both she and her daughters and her mother benefit.
Plenty of posters on here advocate staying at home to raise a child or enjoying the luxury of sufficient income to achieve a work/life balance. It's not a fault not to be financially ambitious. And yet the OPs parents are feckless for doing so even though they know their daughter is financially secure.
If the OP has sufficient funds to ensure a comfortable split of the money then that is what she should do. If her parents blow the lot, so what ? It doesn't affect the OP unless she wants to sit and ruminate over the fact that she could have been richer. Equally, if GGM was alive, OP may well have found herself disinherited for her own circumstances.
OP, the danger of taking no advice from family is the bias that they cannot avoid. Your mother has been cast as an irresponsible wild child. No matter what she does, she will always have the stigma of that and it influences how she is perceived and treated by family. The notion that you have to be true to what your GGM wanted is affected by the fact that you only have other people's memories or interpretations as to what she wanted. And what is what she wanted isn't fair ? She judged a 16/17 year old child whilst rewarding another. She didn't trust her own child to inherit fully. Maybe your GMs view of your mother is affected y the fact that her own mother left to one of her children and not the other. Why is your uncle not considered feckless ? Is every generation consigned to a life of financial sobriety and constraint just so the next generation can benefit ?
You have a wonderful opportunity to benefit from this or you can choose to continue the family rebuke of your parents. If you are going to give to them ( and I do think you should restore at least part of your mothers inheritance to her) do so freely and with a generous spirit - do it without conditions or expectations or rental agreements. Decide on an amount, see it as her money and walk away from the burden and constraints that GGM put upon you.
And OP, one last thing. Why are you going to uni ? Is it for you ? How would you feel if your child judged you some twenty years later for prioritising you own desire to better yourself rather than stay at home spending time the majority of your time with her whilst she was young ? That's the equivalent of what some posters are doing to your parents.