At what age do you feel its appropriate to take a child to a funeral of a distant relative whom they've only met a couple of times?

I feel that would depend on your own beliefs as to the degree of reverence that should be given to those who have passed on.  As parents we most often want to instill within our children those qualities that we feel to have moral and social value.  Death is a certainty in life and children will experience it whether it be with a pet, a plant, or a person.  There is never a good time to experience death so talk to the children about life and give them your best explanation of death and your thoughts of the afterlife whatever that may be.  Their exposure to a funeral will give them something to think about as they establish themselves in this world.  Death is less upsetting to children when they have had at least a little exposure to it and an understanding of it's reality.  Age is irrelevant.

I think it depends on who died as well as the children themselves. I made a horrible mistake when I took my now 7 year old to his great grandfathers funeral 3 1/2 years ago. He wouldn't sit still and of course could understand the magnitude why people were upset. However I had a baby pass away and we did not have a traditional funeral we had a funeral/ burial where all 3 of my other children did great there ages at the time were
1 1/2, 2 1/2, 5. I think because they knew that it was a sibling that they understood they this is a time to be humble rather than bouncing off the wall.