To clarify the situation. Your daughter's partner has custody of the child. Has this been challenged through court? It is more usual for the mother to get custody, unless there are any unusual circumstances.
No relative has automatic access. If a family member wants access to the children they would have to demonstrate that it would be in the best interests of the child. The gp would have to demonstrate that it would be beneficial to the child. If the parent objects they would have to explain why they thought it would be detrimental to the child (disruption to routine, potential violence, abuse, etc.).
Both parties would be saying that it's in the child's interests to have contact/not have contact with X for the following reasons.
There are also the views of the child to take into account. If the 'child doesn't' like granny then I can't imagine any court would force the child to visit them. When alls said and done it's what's best for the child.
Th gps would also have to explain to a court why they could not reach agreement with the parents or, to look at it another way, why the parents were being unreasonable in denying them access or the frequency of access they wanted.
Unless there are exceptionally difficult circumstances it might be worthwhile considering mediation.
The
Grandparents Association might be able to help. They run a helpline 0845 4349585 (M-F 10:00 - 15:30)
The
Children's Legal Centre website has FAQs on contact issues.