AmberGran
I think contacting the GD while estranged from DD may be leading to a whole new problem when DD finds out. GD may go against the wishes of her mum if she remembers her gran affectionately, but the likelihood is that DD will use this as proof that her own mother can't be trusted and is out to cause trouble in the family. I would assume that if DD did not mind them being in contact she would have made contact possible earlier.
If GD has just started Uni then she is only just 18 - much depends on her relationship with her own mother, of course.
OP’s daughter, like those of us here, is now the parent of an adult. Granddaughter is 22. This means granddaughter is entitled to make her own choices. It could end as you say, or it may not. The main point is that having adult offspring, however young, means we have to let them decide relationships for themselves. There are so many estrangements rooted in parents trying to control the choices of their adult sons and daughters. We don’t have to agree with their decisions. It’s their life. We don’t have to approve of the company they choose to keep. We just have to recognize their rights to make these decisions as adults. The OP should of course tread carefully because she may not get a warm response or any at all. But it is that reason which should make her proceed with caution, not the possibility of her daughter being controlling toward the granddaughter. Ultimately we can only control ourselves.