Your father will need to meet with an attorney experienced in representing successor executors where the original executor has the kinds of issues you've described. Unfortunately, advice on how to deal with this situation, and when to do so, is very fact-intensive and beyond the scope of a site like Avvo.
Please note that, while I am a lawyer, I am not your lawyer. This information is for general educational and informational purposes only, and is not legal advice. You should review your particular situation with a qualified lawyer of your choosing.
What about your other aunt? Is she willing or capable of acting as the trustee. Most trusts contain language that allows one co-trustee to act as the sole trustee where the remaining co-trustee is unwilling or unable to act. If your grandmother is legally competent to make her own decisions, only she can make the change concerning her trustee. If she is not, and the other aunt is unable to perform her duties as trustee, your father may need to petition the probate court to be appointed as the acting trustee. Similarly, even if it’s the case that your other aunt is unable to act as trustee but your grandmother, although competent, is slow to make the needed change (possibly due to her medical conditions), your father would still be able to file a Probate Petition seeking to be appointed as trustee.
It’s also possible, if your grandmother is no longer competent, for your father to petition to be appointed as your grandmother’s conservator. But, this is likely unnecessary as she does have the trust that names him as an alternate successor trustee.
Disclaimer: The above answer does not create an attorney/client relationship. My responses are intended to provide general information about the question posted. I am licensed to practice in the state of California. The information provided on this site should not be used as a substitute for conferring with or hiring a competent legal advice from a licensed attorney that practices in the subject area in your state.
An amendment to a Trust is a simple straight forward bit of paperwork, which can likely be accomplished quickly. Your Grandmother needs to consult with an attorney to fix this potential problem now.