I didn't go all the way to Los Angeles, but I went from Seattle to San Jose a few years ago when 7 months pregnant and suddenly afraid to fly.
It's a long trip, I won't lie to you about that. And Amtrak is NOT known for being on time...the longer you are on the train, the more behind you're going to get. They share the rails with freightcars, and if a train ahead of you has something wrong with it, you can't go until they do!
I had a roomette, and if I hadn't been out to *there* and having to go to the bathroom a million times a night, I would have LOVED it. When you get even the cheapest roomette, you're considered First Class, and meals are included, along with a special lounge car. It's veddy veddy nice.
Looks like you'd be on the Coast Starlight (which I rode on my long trip), and then switch to the Pacific Surfliner to get to Anaheim? Sounds wonderful to me.

But then I love trains! We took the train up to Vancouver to get on our honeymoon cruise, and found it to be the most marvelous, stress-free, way to travel (left the day before our cruise, went home the day after, to reduce stress of delays).
Oh, and on my way to San Jose, I was in the first class lounge with a slightly older couple on their honeymoon. They are both flight attendants, but the chose the train to travel for their honeymoon. They were going all the way to San Diego, but just to highlight the fact that the train is pretty much ALWAYS late, they said that they had made the trek many, many times, and they had NEVER been able to catch the last train to San Diego (which would be the Surfliner, by the way), because of the lateness. However, Amtrak would always have a coach (bus) waiting, to finish the trip south, which might mean that that is how you would finish your trip to Anaheim as well.
Or just snag a room in LA for the night and catch the first Surfliner of the morning. (sounds like more fun to me!)
Hope you go and have a great time!!! I can't wait until DS is a bit over 3 so I would think he'd have a good time...