Does my toddler have to sit in car seat on united flight?

FAA doesn't enforce it and it's not a law it's just one of those things that's "highly recommended". It has it's pros and cons. Pros being it keeps the child strapped in the whole time so you don't have to worry about her getting out of her seat and some say it's safer. And the obvious Con being it would be a hle to lug the carseat around with you. If it were me I wouldn't bother with the carseat, just check it in at the counter and pick it up at your final destination with the rest of your luggage.