I would suggest that you invest in one of the Southwest blue bags for $15 (maybe $10? I forget) and you can put the car seat attached to the base inside the bag and it will be easily handled as one item - I'd curbside check that myself, but that's up to you. If the car seat goes into the stroller, then instead I would take the stroller and car seat through the airport and put them in a blue bag for gate check together, then you can use them to get out of the airport too. Agreed with the seat belt straps - if you'll be driving a limited amount or taking taxis/uber/lyft it works well to just use the belts instead of bringing the base along with you. If you'll be driving a long time in a rental car over several days, maybe the base makes sense.
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