I think, as long as the parents (or a suitable designated other adult) cares for a child and removes them if noisy or deals with any upset they have, there is nothing wrong with having children at funerals.
One part of my family are a very much "children should be seen and not heard" mindset - e.g. I was a "child" when my uncle got married (I was 1 month short of my 20th birthday) and it was a "no children" wedding. So the "children" were not welcome at my Grandad's funeral (3 grandkids aged 8, 4 and 6 months, and 1 great-granchild aged 4 - the other 2 GGK were too far distant to travel anyway). Only the "adult" grandkids were allowed (aged from 25 upwards). However, we took DD to the removal the night before (not to the house, where the coffin was open, just the prayers in Church) as we didn't really have other options. DH collected her from creche and met me at church (which meant I had to drive myself, alone, behind hearse - my parents and Dad's siblings were all in funeral car) - he had a packet of buttons and raisins to keep DD happy, and made sure she'd eaten before they got there (I think a happy meal en route), and the colouring pages and pencils in my handbag were used too. She was very good, but he sat at the edge of the row to be able to leave with her if need be.
The day of the funeral though, we did send her to creche as normal and went alone. As she would have been the only kid, and I was not sure I'd keep it together so as we had the option, DH preferred to support me knowing that DD would be happy.
We have a few more funerals likely in the coming year, I'd say. One is the wife of that grandad, and the same principles will apply I'd say (no kids welcome - but we will probably bring DD to church at night as she will want to say goodbye - knows them all well). We will see how we will play the funeral itself - probably leave DD in her normal routine, but she understands more now and does seem to understand death quite well (she reminds me to go and have a chat with my 2 grandads (1 she never met) in the 2 graveyards).
The other granny is likely to have lots of kids involved - all her own grandkids are fully adult, but she has 6 great GKs and 2 step GKs who are early teens and I reckon all will prtobably be there. 5 GGK will be travelling from the UK (well, 3 will definitely come with their parents, 2 may stay home with their dad if mum flies alone) and DD will be there for all too.