Hi OP, you have my sympathies, I would be super stressed at the thought of it.
When I first flew with my son, at 13 months old, I was so panicked that he'd play up, scream, cry, annoy other people etc and I got myself really wound up. The flight was going to be 4 hours long and I was just dreading it. However, it was nowhere near as bad as I anticipated because we were allowed to sit in the row of seats that were by the entrance doors at the middle of the plane so we had loads of leg room, no chairs in front of us and lots of floor space. The airline staff were happy for us to have DS's toys and books on the floor space and then we just sat DS on the floor and he played happily down there for the duration of the flight.
Could this be something you could enquire about? If you don't have a row of chairs in front of you your daughter may not feel as trapped in and be less stressed? The same goes with her potentially having some floor space to sit/stand in, it may just make things more bearable for you if she isn't being made to sit in one chair and feeling crowded for the duration of the journey.
As has been said there are just things you need to realistically consider....
If she's strapped in and starts shouting, screaming, trying to escape during the take off and landing how easy are you going to manage her if you have your one year old on your lap? You keep saying you can restrain your daughter but in doing so is she likely to be kicking out with her legs and arms, kicking other chairs or accidentally hitting other passengers? And again, how can you restrain her with a 1 year old on your lap?
I imagine someone would be happy to hold your baby for you as a one-off, short term solution whilst you are sorting out a problem with your daughter but I don't think anyone would feel happy about doing it for a prolonged period of time.
As a previous poster had said, use ruck sacks for your hand luggage because you are going to need to keep your hands free.
The best of luck OP - I hope it goes better than you think 