Note, I'm not a child mental health therapist, but it's nonviolent, has big cuddly characters, is a FUN film, and has a subtext about dealing with illness in the family in a healthy way.

I'm curious, have you ever seen it?

A bit from the film:

Girls are waiting at the bus stop for their dad to come home, Mei (older daughter) has not yet seen Totoro (nature spirit that looks like a cross between an owl and a penguin with horomonal balance issues, about 8' tall, and cuddly as all heck, with lungs to beat a politician), Satsuki (younger daughter) has.

Dad missed the first bus, Satsuki gets tired and falls asleep on Mei's back. Mei (holding an umbrella and her sister) hears footsteps, sees bear feet, looks up, and there's Totoro waiting at the bus stop with them, complete with a lily pad umbrella.

He notices them, hands them a packet of seeds, and then they see lights off in the distance - and the Cheshire cat bus pulls up, he chirps at them (in the english version, Carl Macek blows into a microphone instead, ruining (IMO) the mood), gets on the bus, and rides off into the distance, while the girls stare in complete and total disbelief.

It's a fun film.