I strongly recommend that you NOT rent a car. Many of the roads are very difficult to maneuver: winding, narrow, steep, and confusing. Some are in very poor condition too. Sightsee from the water.

The local tourist board has good information on their website. You are far better to arrange for a driver, and most of the taxis are vans, so they can easily accommodate your luggage. A 20-mile drive from north to south on the western route can take up to 2 hours. If you or your children get car sick, consider buying seasickness wrist bands for the ride from the airport. No kidding! It's that steep and curvy.... but we'll worth it - a beautiful island

http://www.stlucia.org/

Have a great trip. (I'm in St Lucia right now at Ladera.)