Great, I am glad that you'll be coming to California, as I have a great suggestion for you!
There is a wonderful place in Tustin, about 15 minutes from Disney called The Spaw. They do doggie day-care as well as grooming. Everything is cage free and they have a separate area for little dogs. They are off of the 5 freeway and Tustin Ranch Road (Disney is off of the 5 and Katella/Harbor, so less than 10 miles away)
When my dogs go for grooming they get a couple of hours of doggie day care thrown in and they really like it there. Everyone I know loves it and I know a number of folks who leave their pups there for overnight boarding too. They have 24-hour/day supervision and you can keep on eye on your pups via their Periscope App---that way you can ensure that they are having a great time and can see them on your phone while you enjoy the parks.
During the week they are open for something like 11.5 hours/day and their hours are somewhat shorter on the weekends. Full-day doggie day care covers the full 11.5 hours. They are truly lovely people!
Check them out:
The Spaw Just another WordPress site
If this does not look like a good option, let me know and I can share some other ideas with you and can also suggest some dog-friendly restaurants near the Spaw. I can also suggest some dog-friendly places to eat in Tustin or nearby Orange---I am not as familiar with the options near Disney, but I am sure that there are a few! Overall, this is a fairly dog friendly part of the country and the weather is ideal for Yorkies, so I think that they would enjoy the trip.