You can attempt to soak the water up with towels, but your best bet will be to use a wet vac. If you don’t have one, you can purchase a wet vacuum from a big box store for well under $100. Since you have children, there will be plenty of reasons to use it in the future!
Use the wet vac on the floor and car seats until everything is relatively dry to the touch. Drying with a towel should suffice for locations like the dashboard and cup holders and a hairdryer will work for under the car seats if the wet vac can’t reach.
Leave the car doors open to allow the car to air dry when you finish.