should I seek legal advice before speaking with hotel’s claims department?

If the hotel was at fault in your mother's injury--which, based on what you write, they may well be--they would liable at most for her out of pocket (not paid by medicare, medicaid, or private health insurance) medical costs; lost wages, if any; and possibly a *small* amount for pain and suffering for the broken thumb and having to spend two nights in a hospital. (You typically don't get much for pain and suffering unless and until you are looking at months or longer of significant life impairment.) That's the most she would get, based on what you write, if you sued and won. Typically, if you get a voluntary payment or settlement from the other side without having to go to court, you accept less than that--you accept less, because you save the time, cost, and risk of losing (court is not guaranteed) of court, and the other side's incentive to voluntarily pay you something is that they save money over what they'd have to pay if they are sued and lose.
If that possible amount of compensation is not worth the cost of an attorney, then speak to them yourself--you don't want to spend a large chunk of (or even as much, or more than) what you could recover on an attorney. You also have to have reasonable expectations: if your mother recovers well, as we hope, and have little in the way of out-of-pocket medical costs, you are probably talking a few hundred dollars, not thousands of dollars.