Valencia Travel Village is about 25 minutes drive up the 170 and the 5... so long as you don't pick the absolute worst time of day to go with the rush flow of traffic. Also, so long as there are two of you in the car, you get to use the car pool lane. Even in the worst time of day in the carpool lane, you're looking at 45 minutes. This is a great park that will suit your needs. The monthly rate works out to about $28 per day with all utilities included. All the best to you and yours in this trying time.
By the way... In the LA area, pay attention to travel corridors rather than distance. Getting from one spot to another with some daily regularity often has very little to do with distance and more to do with route.
PS: I can also recommend the Castaic Animal Hospital just up the road. Dr. Connor is the only doctor there, takes his time, knows his stuff.