Sadly, like many of you, I've been in this position with both my in-laws at different times.
At FIL's crematorium service (there was a later church service) my SIL's children were present (2.5 and just 1). All I can remember is my BIL (husband of SIL and not blood relative) just gurning and laughing at the 'antics' of his 2.5 year old who was happily smashing hymn books all over the place.
I was a bit surprised at them being there - but as beloved grandchildren - and as it wasn't my father - I put it down to family differences. However, I did find it exceptionally distracting (the behaviour of BIL and the children). This confirmed to me that I didn't think young children at funerals is the best of ideas because it can be very distracting (admittedly BIL really could - and should - have handled it differently).
Fast forward 4 years and it's MIL's funeral and by now I have my own young children.
I wasn't keen on them coming but the distance was huge (couldn't do in a day, and it would have been unfair on DH to attempt it - or to get him to fly solo) and we had no 'back-up' at home to have them. So I found myself doing something I didn't think I would do and took small children to a funeral (again, a crematorium and church service). It was actually fine.
However, unlike BIL, I was extremely conscious of where I sat and how I behaved - we sat where we could get out if needed, and I took ample distractions for them. I also assumed full responsibility for them as DH was occupied shall we say - although that did mean that my primary focus wasn't on my grieving DH.
It was bearable at the crematorium although I was so heavily conscious of child-distraction that the meaning of the event did get lost. It's hard not to when you've your hands full with toddlers.
At the church service it was very child-centred (MIL was a teacher and did lots of children's church activities).However, the service wasn't enhanced by the presence of several children (including non-family) - but neither was it distracted by them.
Even though it worked out OK in the end, if I had to consider it now with highly active pre-schoolers (who just won't listen and enjoy screaming their lungs out) I may choose to stay nearby with them and pay my respects privately. As many have said you know your child(ren) - and the wishes of those involved. I'm sorry this is something you have to consider (funerals are never easy) but I hope whatever happens that it goes smoothly and that you are able to pay your respects as you wish to.