My car broke down over the summer and had to use uber/ Lyft since. I pretty much load the stroller with the car seat wheel it to the car and put the stroller in front he trunk to make it easy most drivers are very understanding I never had an issue.
I see now Uber has a car seat option, but I just order a regular Uber and bring the car seat and stroller. Sometimes the driver even opens the trunk so I can put the stroller in
Yes I would bring it momma.