Sorry re your mum. (I lost mine suddenly last Feb, but she was a good age.)
I'm an aethist.
I have always been honest about this with our children who are now young adults.
I think children can be quite accepting of death if you are straightforward about it.
Yes, they will be upset when people close to them, (or pets), die. But you will comfort them by saying life isn't forever and when we die we do not suffer anymore. We just ARE no more.
If they say "But mummy, will I die? I don;t want to die!" you can say "remember before you were born? well it's just like that. So it's fine being dead" ... and they usually can accept this after they have thought about it for a while.
Then they might say "But mummy, I don't want you to die" and again you can be honest with them .... ie say that you WILL die one day, (as will they, as will EVERYONE), but hopefully not for years and years. And by then he/she will be all grown up perhaps even VERY OLD, with children of their own? And they will be fine. (Just give the truth with some reassurance.)
Children in developing countries witness death/experience bereavement much more frequently and they also seem to cope. Birth and death = life. It's a simple fact.
And I think making death too 'mystical', (or lying), is a lot more problematic in the long run than being totally honest. (And letting them see the dead pet etc.)