I took Amtrak from San Diego to LA this month (May 2018) for both Dodgers and Angels games. Amtrak stops at Anaheim and the station is adjacent to the stadium and is an easy stroll. Amtrak service to LA Union Station is convenient also. The Amtrak ride to LA from San Diego is about 3 hours. From Union Station, the Dodgers offer free convenient bus service to Dodger Stadium. Again, the well marked "Dodger Express" buses provide a FREE & quick 10 minute ride to Dodger Stadium and drops fans behind your choice of home plate or outfield stops. The Dodger Express service at Union Station is at its own well marked stop at Union Station. Follow the signs or ask the many security employees or the information center near the main waiting room if you're not sure. Plenty of fans use the service but its a clean and friendly ride. After the game, pick up the bus in the same area where you were dropped behind home plate or outfield entrances. Service runs to about 30 minutes after the end of a game. Amtrak offers discounts (ie Military 10%, 50% off for one child with adult fare, etc). However, expect about $35 adult fare each way between Union Station and San Diego. Greyhound is about $23 each way. You'll need to taxi or Uber from LA's Greyhound Station to Union Station. It's about a 35 minute walk and if you're not familiar with LA, it could be an anxious jaunt.
I visited Southern California without renting a car. I loved it. I used the $15 four day pass for San Diego's all inclusive bus, trolley (light rail), and Coaster commuter trains (additional charges may apply on the commuter Coaster trains). I took Amtrak 2 different times to Anaheim and LA. No parking hassles for me, but, I am not intimidated by mass transit or Amtrak. I easily found my way to San Diego downtown, old town, Balboa, the Airport and other sites. In addition, I find Amtrak is comfortable and scenic.
Good luck and enjoy your adventure and ball games.