Firstly my condolences to you and your family, islandgirl - my dad also died very suddenly, about 8 years ago, and I how difficult it can be to deal with that shock on top of the sadness.
My ds3 was about 3 at the time, and he and his brothers, aged about 5 and 7 all came to Dad's funeral in the local church, and then my wonderful mother-in-law, who came all the way up specially, took the boys back to mum's house and looked after them there whilst the rest of the immediate family went to the commitment at the crematorium.
We felt that it was right for the boys to be at the service, and to hear the lovely things said about their Granddad, as well as having a chance to say goodbye to him, but we didn't want them at the crematorium - my dh in particular thought it wouldn't be a good idea.
I think, from what you have said, that you are having the whole service at the crematorium, in which case I would say that you will know best whether they will cope with it.
I would second Katie's suggestion - my MIL sat with the boys and us during the funeral, so she could look after them and dh could look after me.
Hugs
sunnygirl.