How to keep small kids entertained on a long flight?

Demerol works pretty well.

Seriously, I'd recommend having a couple of iPad or other tablets preloaded with educational and entertainment apps geared toward the kids' respective ages. Technology like this has some long-term risks to young children, but for a short duration like this I think they'll be OK. You'll want to make it as easy as possible for them to sleep, of course.

Lemon drops and other candy that takes awhile to dissolve.

Don't forger the headphones and favorite snacks.

If you’re going to do videos or something like that, make sure you do the headphones at home before you get on the plane. I was on a plane once with a mother who tried this and the kid had never worn headphones and it was not a good moment and then she just had to listen to Dora the Explorer, over a speaker until the flight attendant had to tell her that was not acceptable, the whole cabin did not want to hear Dora the Explorer.

It does not necessarily have to be enjoyable to the kids. How would you know if they are quiet. If they are quiet it would be working. Also, I would not worry about educational videos. Anything that your child likes and keeps them occupied and quiet is what you should go for. Not like they are going to profit from one plane ride with an educational video. That said, my two cents would be to use videos as it seems to be the most engrossing thing for children and adults alike and I have nothing else to offer in the way of entertainment that would supersede that.
Oh, and favorite smacks too, a bit of that may add to the a general serene disposition for your child.

Here are a few ideas that worked well for our kids when they were those ages. Stickers, lots and lots of stickers and paper to put them on. Mr Potato Head was a huge hit too. Crayons and paper. I also always brought one new toy for each that they got once we were settled in our seats. Everything I brought was silent, for myself and other passengers;)

A stash of variety of snacks was key too. Although not too many as kids tend to get overloaded when given too many options all at once. So some of their tried and true favorites and then usually a new one as well for backup.

We flew from SFO to JAX r/t at least 3 times a year when they were this young, and these were my lifesavers.

Have you taken any long car trips? It's really the length of time combined with not being able to get up from a seat-belted situation (adults, too!) for rest breaks, rather than mode of transport.
Also, at least your 4-year-old has a paid seat (not sure if you bought one for your 1-year-old?) and is just as much a passenger as any of the others on the flight. I have certainly been seated next to adults for hours who made the experience quite unpleasant in myriad ways, most recently a larger man extending not just his body and his arm beyond the arm rest but his entire leg into my "territory" under the seat in front of me while spilling crumbs from his snacks for almost 8 hours. He also snored really loudly and needed some hygiene! Yuck. I'd prefer a child :)
Assume all will be well!
When the seat belt sign is off, take some very slow circuits around the plane.
Be thankful for digital distraction! Even if you limit it when home. A much younger seat neighbor on another flight watched Paw Patrol on repeat til they fell asleep. The idea of trying the headphones at home is a great one!
Lots of coloring and some quiet new toys is what I did, too, with success, as well as constant snacks.
The idea of hard candy ( a choking hazard anywhere) is not a good idea.
Supervised lollipops, though, if the take offs or landings are a problem (I was still nursing at age one- you could do juice boxes).
Have a safe and wonderful family trip!

Bon Voyage--I agree about the lollipops, especially the supervision part:) I know one man that carries a few in his carryon in case he is next to a child and this might help. Of course he asks the parents first.

I hope your 4 yr old likes to color. If so, never underestimate the value of a new coloring book. It also works when your child is sitting on the curb waiting for the parade at Disney. Also your 4 yr old can wear a little backpack and roll his own little luggage.

Reusable sticker books
https://a.co/d/3vC9lfR

Wiki Stix
https://a.co/d/82sPo7r

Lacing cards
https://a.co/d/4I5IOZ0

Water arcade toys. Add water after going through security.
https://a.co/d/cN3yCkb

Lots of activity before the flight. Maybe they’ll sleep!

When our three kids were young & we flew to see relatives, I had a “survival backpack”. LOL! I would bring out a new item every hour. Years later, our kids told me that our flight days were almost as exciting as Christmas morning. ; )

Some items I remember packing:

• Hot Wheel cars
• Go Fish cardgame
• Small My Little Ponies that came with a little crib & comb
• Small Playdoh container
• Sticker books
• A new storybook
• Paper to be creative, i.e. create a game or origami type thing
• Snacks that didn’t melt or get sticky