Given the ages of your children you will almost certainly need an SUV or minivan to accomate their three car seats (I'm assuming you have at least booster seats for the 2 older ones as they still should be in one.)
Also, the vehicles found on any Exec aisle can really vary at any airport. I would never count on there being a SUV or minivan available. (For instance, on my recent trips to Newark, only sedans have been available.) I would really go ahead and book the size you need. Check out Mousesavers.com's rental car section for codes that can be used for different rental car companies.
Also, I know when you are a loyal member of a rental car company that is hard to even consider renting from someone else. You may want to consider checking out the rates of other companies such as Alamo or Enterprise (Enterprise can earn you points on Emerald Club as well sometimes) to see if you can get a better rate to keep your costs down.
Smart advice!!!! BTW, just for the record: Alamo, National and Enterprise are one company. Different business models, but, owned by Enterprise. We also share cars.