If I go to court to find mom legally and mentally incompetent, can I have legal access to her trust and will as if she had passed?

Her level of competence has nothing to do with her rights as an heir. She may need a conservator herself, but it should not be you since there is an obvious conflict of interest over the property. Listen to your attorney.

It's my mom

Why do you want to be caregiver to a mentally unstable individual?

What's the real issue here? If your father is deceased, and if you were named the trustee as well as the personal rep or executrix of his will, then you have authority to handle his estate now. And you have the obligation to follow his wishes.

What were the issues for the court appointed conservatorship for your father?

Why would you need to go to court to have your mother declared incompetent - do you feel this is necessary to distribute assets to her?

If you're caring for her in Texas, are you planning to move to the farm in Kansas and your question is whether or not you can move now or must wait until your mother passes? How does a declaration of incapacity affect your plans?

I don't really understand your concerns - could you elaborate? It'll be easier to understand how to answer your questions.

I think there's more information that needs to be shared.