If you feel your dc should be there, then that's your call. I agree with you - it was important for me that my kids came to my mil funeral. Mil family expressed concerns about the kids coming, but afterwards agreed it had been the right decision, and certainly at the wake they were a joy and brought comfort to lots of people, even those who didn't know my dc - everyone knew how much mil doted on them.
BUT YABU to expect your mil to look after them. It would be wrong imo to insist they're at the funeral, but not to sit with them yourself. It's not fair on mil to expect her to cope at the back with 2 kids who are potentially frightened by the setting, the emotion & the fact they're at the back where they can't see or hear properly, and probably going to kick up cos they know you're up front. It is a fact kids behave better at the front anyway.
Bottom line is, you want them there, you take them. Can't your dh look after them at the back if you really don't want them at the front?
Oh, and I know your mum is probably wracked with grief at the loss of her mum, but she is being unfair complaining about your mil not gareeing to this. You would do well to ignore these comments, as it is potentiall stoking an anti-mil fire in you that could burn for a long time.
While it is not for your mil to make the ultimate decision, it is also not her duty to look after them if you insist they should be there, it's yours. She is not BU.