Have flown with an infant in long-haul J 8 times now -- LAX-BKK / BKK-ICN-NRT-LAX at 11 months; LAX-LHR-LED / BRU-FRA-LAX at 19 months; and LAX-ATL-FCO / FCO-CDG-LAX at 23 months with our first child and LAX-HND / HND-LAX at 12 months this past summer with our second.
A lot of your experience will depend on who you are flying and the seat/aisle configuration. Of the 8 long-haul segments we have had an empty seat next to us twice, so that can be a nice option if there. If you have a CARES harness bring that just in case for the older one. But I would not bank on it.
Our most recent flights were on Delta 777s which have a 1-2-1 configuration. Those herringbone style seats are actually pretty narrow, which would have been an issue with the baby -- but we choose the second section of J and the last row of seats which have this extra stowage space in addition to the normal seat layout -- so with three seats we effectively had a small section to ourselves - that allowed for some walking down the aisle without bothering anyone else. Plus on the flight there our cabin was pretty empty so we had a whole side of the J cabin to ourselves -- I probably spent an hour sitting with my 12 month old in the aisle while he took the water bottle out of the holder, dropped it on the floor, and then put it back in. Having that space was nice. Try to find a recent Youtube video with your exact flight/plane configuration and see if any seats have any extra space vs. what you might expect from the airline seat maps or even seat guru (i.e. on seat guru these are just labeled regular DeltaOne seats - no indication of the extra space).
Going back to the water bottle -- definitely have a plan/bring some things in case you need to distract them. No matter how good they are, on a flight that long there will probably be a period of restlessness. The water bottle got me by on the flight mentioned above. On that first Thai flight it was playing with the TV remote for an hour in the middle of the night. On our recent LAX-DFW-SJU with the now 18 month old as a lap infant in domestic F it was an ipad and
Duck Duck Moose Old McDonald that did the trick.
We bring our Luna Lullaby pillow onboard - that is mostly how we handle sleep. For the 11 month old it should be big enough to have them rest on it and let you have one, if not both hands free. Not sure about the 23 month old. We also bring the Baby Bjorn in our carry-on as I put the baby in that to board since we fold up the stroller and put that in a gate check bag -- the carrier lets me have both hands free to drag the stroller to the door and still pull my carry-on. Since we have the carrier with us, I have used it a couple times in flight to help get the baby to sleep and once to even be able to eat (ate while standing up)!
Speaking of food - eating is difficult. If sleeping usually not enough room to get the tray out. If awake there is the risk of pulling/knocking things over. Even with my wife and now my older son having their own space and able to hand things to me, I usually have the flight attendant just bring me each thing one at a time and eat one-handed.
Hopefully the two infant in arms 10% fare tickets did not set you back too much (or you are flying AC!)