M.T.
I know when I traveled with my twins from Germany to the West Coast I tried to start adjusting them to the West Coast time a week in advance. It's not easy to do and it can be exhausting and confusing for a kid that young to be awake at 2 or 3 in the morning. BUT it really helped for my kids at least. We were stateside for about a month and I think they adjusted to the time change in a matter of 2-3 days which was really good. My suggestion would be to at least try and adjust your toddler at least to a 7 hour difference if not the whole 14. At least by doing that it'll be easier to have them adjust once at your destination.
As for keeping them entertained I find it to be trickier at that age. My twins are 2 1/2 so I just bring them a backpack of new and favorite toys and tons of snacks. I don't know if your toddler is walking yet but be prepared for the kid to want to move around a lot. I know when I flew international with my twins at 8 months and then 10 months they were learning and then already crawling. It was really tough on them because they wanted to move and we were kinda limited because of the plane. My suggestion would be toys, snacks, and their own seat so when they get restless to the point of you can't get them to be sorta calm and you need a break you can strap them into their carseat and get 5 minutes of relaxation. I know when my kids were restless like that it tended to calm them down and then they'd fall asleep. At least for my kids when they behaved like that it was really because they were tired and not because they needed to play.
I hope some of my suggestions help. I've traveled with my twins international several times since they were three months old and I've even done a few trips solo with them. Just be patient and try to remain calm. I know my first trip solo with them I was so stressed out that other passengers would be rude that it stressed them out and made for a miserable trip. Remember, kids cry and they get cranky, just like adults do. But somehow when in an airplane it's more acceptable for the adults to be cranky and not the kids.