I have had to name change to avoid recognition and join this thread, as my sister in law did this at our gran's funeral.
She decided to bring along her 3 year old daughter "as it would be a good experience for her". She asked what I thought and I said I thought it was a bad idea as her husband was around and could look after the child, and that the child had never even met gran so didn't know her.
She said that she had asked my parents and they didn't mind, so she was going to bring her.
At the funeral, the daughter ran around, shouted "what's in that box" and when asked when to come away she had a full on tantrum in the aisle shouting "no no no" at the top of her voice. I can hear you all saying badly behaved child, but she is not normally like this, and the unusualness of the situation, and the upset people around her affected her.
My mum was particularly upset by this, as she had felt railroaded into agreeing when asked by SIL if she could bring DC to funeral, as she felt to refuse would seem she didn't like SIL.
So just for the benefit of all of you on her that think taking your DC to a funeral because you think everyone else will look upon them with the same indulgence as you:
A. Whilst it is good for children to learn about death, under 5 is too young to take to a funeral.
B. Funerals are not there for you to avail yourself of a "good experience" for your precious child, but for people to grieve and show respect for a loved one.
C. Not everyone finds a boisterous child "a joy" at any occasions, they do not add lightness to the proceedings, and they do not comfort from the new life/death point of view, no matter how much you love their smiling little faces and funny things that they say, this does not necessarily apply to people grieving, and wanting to reflect and perhaps talk about the deceased, not have your child as the centre of attention.
The OPs husband could clearly take the children somewhere else during the service/comittal.