Please tell me what is the normal way that a parent's assets and property is dealt with if she has 3 living children and 1 child that passed away who has children -- also her husband has passed.

Any question on law needs to include the general local as laws vary by area.

So mother died without a will and leaving 3 living children plus some grandchildren, but no spouse?

And those grandchildren include children born to the deceased child?

As ScottGem says, it depends on the intestacy statute for the state or country where she resided at the time of her death. It would be a waste of time to even guess without knowing that bit of info.