Have you thought about renting a car one way, or renting a car for the duration? You might price it out. It's about 95 miles and 1.5-2 hours travel time.
Another option, and this might prove more economical, is taking Amtrak from San Diego to the Anaheim or Fullerton stations, and then taking Uber to the hotel.
https://www.amtrak.com/pacific-surfliner-train
Here is information about Limos.com from
MouseSavers:
Limos.com
For a private ride to/from the port, try
Limos.com. They will get you quick quotes from up to a dozen competing companies and you can even read reviews of the various companies before you request the quote.
When requesting a quote through
Limos.com, the airports are obvious, but the location of the Port of San Diego may not be, if you’re not familiar with the area. For Port of San Diego pickups and dropoffs, you would select To (or From) Cruise Port, then type “Port of San Diego.”
- Get $10 off airport rides with Limos.com. Use code AFF13$10.
You can also just try Uber (check pricing) or a taxi.
Here's a link to Roadrunner shuttle - you can get a free quote:
https://www.rrshuttle.com/disneyland.html#