Who has the rights to my great gandfather's minerals?

Seems more like a legal matter than a minerals matter. First, do you have a copy of the family trust document? Then you need to see where you fall in that trust. We had a similar situation but the trust was automatically terminated when our parents died and the assets distributed to the heirs named in the trust. It would seem that since you are not a trustee there is little you can do but you likely need a lawyer to sort it out for you. Many lawyers will give you an opinion of what will be involved at no charge for initial consultation.