Southwest sells re-usable big blue bags for $17 that you can put strollers or car seats into when you check them. (Or both might fit in one bag.) You can also buy your own bags elsewhere and use them. It is your choice to check any of these items at curbside, the ticket counter, or gate check - mainly if you want to use the items inside the origination and destination airports then go with gate check, otherwise there isn't much difference. For gate check, you'll go through security like normal and when you get to the departure gate go up and request a gate check tag - they can put this on the blue bag if you choose to buy one - you need to do that before boarding so that you can drop the checked item at the end of the gangway, don't wait to get your gate check slip and to wrap the stroller until people are already lining up. Two adults can board with a young child between the A and B groups.
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