There is car rental on site at DLR. I believe the office is at Pardise Pier. You could forego the car rental for the Disneyland part of your trip, but then rent a car for the San Diego portion. The drive to San Diego is not bad at all, and the traffic in San Diego is no where near as bad as Los Angeles. It is not hard to drive in that area at all.
Outside of a car, I would take the train. We were in Los Angeles last week and one of our drivers said that the farthest trip he ever had was from the DLR area to San Diego. He did say a lot of drivers will reject the 2 hour trip, but that some will take it. My guess is an uber from DLR to San Diego one way would probably be around $150. If you need an Uber XL due to luggage, I bet it is closer to $200. For those prices, you might as well rent a car, especially if you are driving back for your flight home.
We typically spend 5 days at DLR and then go south to the San Diego area. We usually rent a car for that portion of the trip. We typically drive back to SNA to fly home. That is because we have friends that live about 30 miles north of San Diego, so we usually stay in that area. From there is it not that much of a difference to just go back to SNA and the car rental can be cheaper if you return to the same place instead of a different drop off.