I can't agree with you as far as the grandmother having to allow the unsuitable (?/unstable) mother to make the decisions.
I do accept totally that there are fifteen year old mothers who are quite capable of doing a good job, but isn't it obvious that this grandmother has picked out a figure to illustrate the immaturity of her own daughter at twenty nine, and her lack of progress to that supposed mental age (she could have said "ten year old" I guess).
I would hope your authorities would welcome the grandmothers interest in their grandchild - it wouldn't be the first time would it, that a grandparent has stepped in where the parents failed for some reason.
As far as advice or sources of advice for this grandmother goes, I would say professional help, if you can afford it, should be taken. If you can't do that just present yourself and granddad I presume, as well as possible to the authorites who will be no doubt interested in your desire to look after your grandchild.
Graham