okay - we fly ALOT with the kids. They've both done in excess of 50 flights now and are 4 and 2.
I dont know what your airline is like
ut I'll give you what we've had and done.
We do as early check-in as possible. Get decent seats, PREFERRABLY BULKHEAD so you can get up and down and have some space. request bulkhead seating at check-in.
go get seated in a nice restaurant in the airport and have a good BIG meal, wastes alot of time, stuff them full of ice cream etc. Helps them SIT on the flight!!
For the 10 month old - with our flights we used a skycot which was attached to the bulkhead wall and he slept in one of those till he was 12 months old. I dont know if your airline has those so ask them.
we always bought a ticket for the boys from age 1 onwards. you can either use your carseat or ask if the airline has a special booster seat. The carseat is the better option as they are used to it. You will be required to seat the baby in your lap whenever the seatbelt sign is on however. If the flight is shorter than say 3 hours - probably dont buy a seat for the baby and just have him on your lap .... anyting over that time and you'll be begging for a rest.
I know people who have slightly sedated their kids on flights with things like antihystamine .... we enver needed to.
If your kids go wild and scream and cry and are unhappy, just try and soothe them. As a mum in a confined space with an unhappy child I know what can happen and once spent 5 hours out of an 8 hour flight in the toilet with our baby coz he wouldnt stop screaming!!
I was so worried about the other passengers - but **** happens - bring everything you know he'll want, and try to be as relaxed as possible as he'll pick up on your stress and react.
take a change of clothes for him, just incase of a little sickness, and a dummy or bottle to suck on during take off and landing to help the ears pressurise.
walk him round the plane, the FA's should let you and that keeps them very happy looking at loads of poeples faces!!
order childrens meals or bring your own.
book a porter to pick up all your luggage, and take the stroller all the way to the aircraft door and check in there, you'll get priority boarding as with a small child and pick up the stroller as you exit the aircraft so you dont have to walk with him carrying him to the baggage claim.
thats all I can think right now - I'm sure theres more though!