Sounds like she wasn't mature enough and physically big enough to sit in her own seat. We used car seats for both of our kids until they were about 4yo. Reasons: 1) safety - if we hit bad turbulence, which we have, they would be as secure as possible in their 5 point harness 2) because they use a carseat at home, there is no expectation of NOT having to sit in it - it's just wasn't something they considered. If they're flying they HAVE to be in a seat, just as if they were in a car and 3) their carseats are comfy so this made playing and napping easy for them.
I can see why the FA was concerned...since she was over 2yo, she shouldn't be on your lap. This is an FAA regulation. I can totally see it from your side too though. She was getting ansty and it was getting bumpy and you wanted to hold her. Certainly understandable. I'd try the carseat next time. Good luck!