Assalamu Alaikum, I would avice that 2 year old's minds should not be corrupted by the Cartoons, this is the time they should be treated their age. Let him be him, he will not be 2 or 3 or 4 etc. ever again, so let him act his age, play, make a mess, bother you and everything that is attached to that age. As for keeping him in one place, why would anyone want the child to be in one place.
Alhamudlillah a healthy and active child will move around, explore and learn. Putting him in front of the TV. to watch some cartoons will not do him any good, will just make him lazy and take away his imagination.
Forget about having free time for yourself, when this child grows to be 12 or 13, he won't want to be watched by you or anyone, they start keeping to themselves, and it's no use trying to force them to be in front of us at that age.
Enjoy your 2 year olds terrible two's, with time you will appreciate that you were there enjoying his tantrums and all, because those days are not coming back.
One of the thngs that you can do is get books and read to him and explain to him in a way he understands., and teach him little things, at age 2 they are great helpers, just ive them a wet itchen towel and show them how to clean the walls, soon your walls will be sparkling and your floor squeaky clean. Give them a pencil and teach them that they have to use them only on the doodle pad, and see how many masterpieces you will have within a day. these will be precious memories for the future inshaAllah.
Did I do all the things I am saying??????, YOU BET IT, I DID AND AM ENJOYING THE MEMORIES NOW, BECAUSE THE BIRDS ARE IN THEIR OWN NESTS NOW.
There are 2 year old children out there who are not active and cannot move and don't need to be disciplined or anything, May Allah have mercy on those parents. Let's be thankful to Allah for giving us healthy childen and do the best for them in all phases of their lives. May Allah accept our efforts, ameen.