Hi there! We have done this a couple of times, it's really easy to do and fun! There is an Amtrak station in Anaheim, we just took a taxi from our hotel to the train station, (it wasn't far from where we stayed) and then took the train to downtown San Diego. Our hotel had a van that picked us up downtown and took us to where we were staying, but it all depends on the hotel you will be staying with as to whether they have transportation from the train station, you can always ask! The ride along the coast is really nice and relaxing...Amtrak only goes to 2 stations directly, downtown and Old Town, if you want to get to Seaworld you would have to take a bus from one of those 2 stations, but I would imagine you would want to get to your hotel first and check in before doing the parks. Also, if you haven't considered it, I would highly suggest
Legoland, especially for your child's age. We took our kids when they were a lot younger and they loved it! It's in Carlsbad, right along the coastline. All the rides are geared towards little ones. Good luck with your plans and welcome to the U.S.!! I would suggest Business Class, for a small additional fee, here's some info on it:
Business Class Seat
Business Class Seat Upgrade for Less
If you've never upgraded to Business Class on Amtrak, you might be surprised at how affordable it can be. Business Class is offered as an upgrade on many of our long-distance and short-distance trains and is the minimum class of service on Acela Express. All Business Class seats on all trains are reserved. Check out the upgrade options when booking your travel to make your next trip more comfortable and productive.
Comfortable headrests and footrests Ample legroom Conference tables or fold-down tray tables Overhead reading lights Standard AC electrical outlets for every pair of seats Complimentary newspaper and non-alcoholic beverage (served in Cafe Car) available on some trips.