There are some families out there who think everyone should gather and attend regardless of age. However, I think it is something the parents should decide. It won't hurt her to attend, but it won't do anything for her, either. She's only 2, and you'll spend half your time keeping her occupied during the service, rather than actually paying attention yourself. Go with your gut. Especially if you would also have to watch like a hawk to be sure someone didn't feed her something she shouldn't have. Be prepared for your mother in law to be upset with you, but maybe your hubby can be the one to break the news to her, so it's family to family, versus an in-law battle. :-) Frankly, I think a child of any age could go, but the decision should have more to do with what the parents are comfortable with, and obviously you are not comfortable with this idea. Could someone on your side of the family babysit, or is there some good friend who would enjoy your daughter for that day ?
Good luck. Emotions run kind of high at these times in people at these kinds of times. You'll laugh, but when my 25 yr old niece came, we brought our kids (10 and 12) to the visiting hours, to stay there the whole time and my mother thought "it was no place for children". So I checked it through with my niece's more immediate family, whose response was, "I don't do well at these things, and having the girls there will help me cope." So they came, they did just fine, and they helped their older cousin have something other to do besides talking with people she didn't know. At their ages, and given the fact that they didn't know her all that well (she was the wife of an older cousin), and given who my family is, it was a safe time to learn abour death, and it went very well actually. But they were a WHOLE lot older than 2.
You have good instincts, Mom. Use them.