If you are driving directly South on I-15 to San Diego, you can take the I-215 split off in San Bernardino to the to I-10 east, a few miles to San Manuel.
You can continue on I-215 south to San Diego and rejoin I-15 in Temecula, or go west on the I-10 back to the I-15 south to San Diego.

In Temecula, you can easily get to Pechanga.
A little south is Pala.
If you're willing to go 20 minutes east of Pala, is Pauma, Harrahs, and Valley View.
If not you can continue to San Diego on I-15.
The back roads from Valley View will take you to Escondido which will connect to I-15.

There are several in San Diego, look them up for casino's near where you are staying.
Barona, Viejas, Sycuan, Jumal are all far apart from each other.

If you have a lot of time, an hour east of San Manuel on I-10 is Morongo, another 45 min is Palm Springs, Spa Casino, or another hour east are several casinos, Auga Caliente, Fantasy Springs, Spotlight 29.
But these are really way out of your way from San Diego, especially with kids.

If you want an easy stop over from Vegas, then just take the I-15 to Pechanga (5 min off freeway) and Pala (windy road 15 min from freeway).
The city of Temecula is about an hour from San Diego, and 5-6 hours from Las Vegas, depending on how you drive.