To your question, OP, I think the best course of action if you're really unsure is: Ask someone else who is close to your cousin/familiar with how the funeral is being planned and see what they think. I wouldn't bother your cousin with this, but maybe try to find someone who is more closely involved with the proceedings than you are. There is also the separate issue of "does this rise to the level of taking my child out of school," which is something only you can answer. Your instinct seems to be that yes, it was, so I'd say go with your gut.
I'm American (married to an English man who now lives here in the US) and for me, too, it has been very surprising to learn about some British attitudes toward children at funerals. Not that it's wrongobviously every culture gets to make its own rulesbut very, very different. I have attended funerals from before I am able to remember (so a very young age) and I would never expect anyone to leave a child of any age at home in order to attend a funeral. Of course, I would expect them to take the child out of any proceedings if they became disruptive.
In my circles, childrenespecially little onesare very welcome at funerals because they bring some levity and happiness to an otherwise sad situation. It's also a sign of respect to the family--if my family were invited around to someone's house for a holiday gathering, and I didn't bring my children, I think it would be perceived as a little odd.
Culturally, though, we are as a people liable to turn up at just about anybody's funeral. Did we work together more than five years ago, but we are still friends on social media and I just found out your dad died? OF COURSE I will show up for the wake. Not long ago, our entire office basically closed so we could all drive several hours away to our colleague's father's funeral. Obviously we had never met the deceased, but we knew his son (our coworker), so why would we not go? It's just a way to show the surviving family that there are lots of people in the community thinking of them at a hard time. I literally would not be able to count the number of funerals/death rituals I have attended.
My husband and I are currently engaged in this discussion because we have a funeral to attend in the coming weeks. I assumed our 3 year-old was coming, he assumed our 3 year-old was staying home. So we will see how it plays out!