It is uncertain how title to the property is being held right now & also if the estate/probate are still open. That will determine the answer.
Is the property still in the name of the estate or has it been transferred by means of a Quit Claim Deed to both of them being in title?
If he is a co-heir & her executor papers are still valid (estate is not closed yet) (also if probate is still open), she very well could have power to sign if the estate has not been closed yet.
If the probate is over and the estate has been closed, she is free to list with anyone, but any agent that accepts the listing without the signature of both owners may have a rude awakening. If she is presented with a full price offer from a ready, willing and able buyer and your husband does not sign, the cousin is the one on the hook to pay the agents their commission, even if the offer don't come together, should they choose to go after her.
The property can't be sold (transfer title) without signature of all owners of record.
FYI, executors are allowed to charge for their time & services for handling an estate. Most greedy ones do. Others do not.
From a question you posted 3 weeks ago, it sounds the aunt recently passed away. If this is the case, probate must still be open. The cousin can list & sell the house & may need to do so to settle the estate so that the house can be sold to pay expenses and then she & your husband will split the proceeds. If believe there is any funny business going on, request a full itemized accounting of the expenses.