Amazing Tales is THE best way to start playing table top RPG'S with your children. Firstly there are examples on what to expect and how to play with young kids. One example, dont plan a big campaign. It's moment to moment story telling and roleplaying. The dice mechanics are simple to learn and characters just have 4 skills. No attribute scores, inventory, or hit points to worry about. With the tips in the book your kids will learn to make fun and creative characters. I recomend the PDF as it will not take you very long to read it front to back. You will not need to refernce the book for skills or monsters. There are 4 sections for settings which have sugjestions but most can be noted for when you play. The best part is children can take any show or books they love and be or create a character for that setting.
My daughters game is centered around a Pirate that can shape shift (so over powered but thats OK and part of why this system works). Most importantly she says that this is her favorite game. We get to spend more time together and enjoying a hobby. It's like being able to tap back into a childs imagination and let go of the what is or is not possible. Have fun and I hope you try Amazing Tales.