I am not a lawyer so my reply is worth exactly what you paid for it. We are also part of a trust. Because it is a trust, we do not personally own the assets in it and we have no say in what happens to the assets - the trustee is in charge. We cannot sell the assets.
That said, we would not sell our mineral interests even if we could. They are too valuable.
Give your Dad a big hug. He is not being lazy but is protecting your interest. I am dealing with the multitude of problems created when an interest was sold out of a trust under pressure from Beneficiaries. It creates a mess for the Trust, may be illegal, creates huge tax problems and legal fees. Don't go there. It is not worth it for anybody except maybe the lawyers.
By the definition of the a Trust, you do not have anything to sell. Be happy that you are a beneficiary.
Yes, if we were broke the trustee has an obligation to ensure we did not starve. They can sell assets to ensure that. If they did not do this, we could fight the trust. Fortunately we are just fine!
The above case does not sound like a survival/destitution issue.
If I am misunderstanding the whole thing, I apologize.
Let me add something here. It's a Revocable Trust so you have no control. Your Father has the rights to all its assets. One day he may need to sell your minerals, or some or all the Trust's assets to support his medical needs. Have you ever thought about that? Don't count your eggs before they hatch.