Sympathies on your loss.
A couple of points - there is no such thing really as a will "needing to be read". Thats just a thing from the movies.
I guess you are really asking does any action need to be taken on the will. That depends on what the assets are, how much they are. and how they are owned at the moment. So if your Dad had assets such as house/land, bank accounts, shares etc in his own name your Mum may not be able to get title without taking out probate. But as I say a lot depends on the assets......
However if your Mum's concern is whether she needs to do something urgently the answer is probably no. She can recover a bit and then take whatever action she wants as long as she has access to whatever financial resources she needs.