I'm sorry for your loss.
My feeling is, take them both, and answer their questions frankly. This is the main way people learn about death, and you get a chance to really shape their understanding. We are very literal about this in our household (the body stops working) but also talk about what we believe.
The 4 yo would likely be more upset by everyone else in the family being upset, then absent, then back and upset again than by what is likely to happen at a funeral. Having a chance to understand where grandma went brings much better closure, and ultimately understanding, than having her simply disappear without discussion or farewells.
If MIL was sick, you might use superlatives to avoid confusing the 4 yo about degrees of illness-- that is, not "gram was sick and died" but "gram was very very very sick, not like that time you had a cold, so very sick that she died."
A 4 yo will probably absorb only as much of what's going on as she can handle, anyway-- the rest is likely to go over her head. At least it's that way in my family.
DeeDee