Hi caala001- You can gate check them both, car seat and strollers. If you'd rather bring your car seat onboard with you, that's allowed too. If you aren't purchasing a seat for your child, you can ask the Customer Service Agent at the gate if there are going to be empty seats. If so, you can bring it on without charge. Otherwise you can gate check them both. You can gate check a stroller of any kind (yes, even those foldable wagons). Just make sure everything is tagged with your destination tag. Then just leave it in the jet bridge as you board the plane. I believe as two paying passengers, you and your husband can each check a stroller. I always say this, but in the case of potentially using a car seat aboard, you want to make sure to use Family Boarding (between A Boarding and B Boarding). You would need the extra time to get your seat installed. Hope this helps! Happy travels! P.S. Here's the info about gate checking - https://www.southwest.com/html/customer-service/baggage/carryon-bags-pol.html About halfway down the page.
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