This is a very tough one. Most books start with disclaimers about characters not being actual people. Yet there is a running joke in the writing community that if someone does something, it is likely to be used as inspiration in our next book, or something we write. That whole things you say and do will be used against you in our works!
Now as normal, I am not a lawyer, and thus I don't know the right legal recourse, but there are a few things that come to mind. If you're writing about her life (like a biography) that's one thing. If you plan on using her name, and again telling about her again that's a thing. If you are going to have a character that does not have the same name, and the story is not exactly about her life life, but maybe has certain character traits that's another.
As you're thinking of using this as a method of showing tribute, no matter how you plan on doing it, it may be worth still reaching out to the son and speaking with him. You could address her impact on your life in a forward or an acknowledgement as well.
I don't know of any writer who can honestly say that every character they have is not inspired by someone they know. But in your case, for this situation, if you want a legal thing might want to check with a lawyer, but I would also state bring it to the son, and let him know how his mother inspired you, and maybe include a massive thank you to him, his family, and maybe her in the forward as well.