A.V.
I would talk to all parties.
We went to the UK and Ireland this summer.
1. Don't expect them to let you use your own carseat on the plane.
2. Don't expect an airline version to be available (Virgin Customer Service has no idea the reality - there are often just 2 seats per plane and they go to the smallest kids).
3. We had no issues checking our seat (Britax Marathon). We used the airport carts to get it to baggage and every time it was checked for free. You will want a bag for it (we got a padded one without wheels). Most of the time the seat was even put in a special area for more fragile items and went on the plane last. We rented cars throughout the UK and Ireland and were happy to have our seat that we were familiar with and that she was familiar with. Also, there was no wondering if someone soaked the straps or forgot to report something. It was a much better experience than I expected and I would do it again.
You can also check your stroller at the gate and re-collect it there from the gate when you land. I had a bag for that, too, but many people did not bother.
As for the flight itself, I didn't get much sleep while DD was awake, but we put her between me and DH whenever possible or on the window seat so that if she woke when I was drowsing, either someone else was there or she'd likely crawl over me to get out. On no flight was it an issue and she did much better than I expected. She was not quite 3 at the time.
