I have just done a funeral this week and children were there and parents either took them out or stood at the back.
The dress code for funerals is usually neat casual unless you know otherwise. On the other hand we have had people turn up in their work clothes as they are there just for the service before returning to work. I think people accept this and people who are casual as many are there to pay their respects before going back to work.
I think the main thing with children is as long as they are quiet and not disruptive then they are fine to stay in.
If it is a family/close friend funeral get someone who knows your child to come along and mind them during the service.