Unfortunately, anyone can file a lawsuit and contest a trust. Some trusts are drafted with no contest clauses which purport to disinherit a beneficiary if they contest the provisions of the trust. These types of no contest clauses are enforceable in some states and not in others. I am not sure about Michigan. In order to determine what his chances of success would be, an attorney will have to review the trust documents. At this point, it sounds as if you have merely a threat and no actual dispute or controversy. Perhaps the best thing to do would be to consult an attorney and find out what the possible outcomes are and simply wait for your uncle to either take action or not.
As Attorney Smith stated, anyone can contest whatever they want. There was an attempt a couple of years ago to make no contest clauses "iron clad." But the courts (and many of the lawyers) in Michigan were resistant to this, so the current law is that the clause will be upheld, unless there is reasonable cause to bring an action.
What that means is that the door is wide open for someone to bring any kind of challenge they want. Will they be successful? It depends on what they are trying to achieve. If they want to get a share of the estate, they may not be able to do so. (This is an area where the facts of each case are critically important. Medical records, attorney testimony, etc, will dictate whether or not your uncle's claim has any hope.)
But if his intent is to tie things up for months, (or perhaps years), and to make life for your mother as miserable and as expensive as possible, then he certainly has an opportunity to do so. It is clearly not what your grandmother would have wanted, and her intent is absolutely likely to be frustrated. But that is the current state of the law. Depending on what is in the trust and how much your uncle is looking for, it MAY be cheaper in the long run to pay him something to make him go away. That is what you need an attorney to advise you on.
Best of luck to you!
If grandma was of sound mind and not tricked or coerced into the trust, then your uncles claim is weak. If there was a strong likelihood of formal litigation, I might consider a letter to the uncle explaining the weakness of his position. This could be helpful ammunition for a counter claim for an abuse of process, or a claim for bad faith, if litigation ensues. It can also discourage an attorney who might otherwise take a shot at the case for either a contingency fee based on a percentage of the estate, or an otherwise safe hourly fee. Incidentally, the buck for your uncle may not have been out of spite, but instead because some attorneys feel that helps prevent a claim by the uncle that he was accidentally forgotten.