I think there are two things at play. Firstly it's definitely normal for a two year old to be throwing tantrums. Have you heard the phrase "The terrible twos"? :)
Secondly it's fairly common for younger children to have a period where they act up after returning from the other parent's house. How is your relationship with your ex, are you able to talk to him to try and make a united front and work out a behaviour management plan so that things are consistent? I think it's also hard for them because they have so many mixed feelings - they love both of you and want to spend time with both of you but it's hard to have that feeling of leaving, even though they know it isn't forever. My son went through some separation anxiety at that age when I left him with the childminder. He always cried when I left and then when I came back, he didn't want to leave!
It would help if you can both try to do some preparing for him. If you have the same schedule every week you could perhaps try something like colour coding. Mummy's house is red and Daddy's house is blue. You could even try to make sure that things he has at each house are always colour coded (cups, etc) Obviously he won't be able to read yet, but you could get one of those charts for the wall with the days of the week on in big boxes and show him "Monday, Tuesday, Wednesday are Mummy days and Thursday, Friday, Saturday are Daddy days." Obviously replace with whatever day it is. If the schedule changes every week then colour coding could help even more. And perhaps a little picture of a boy to stick on the current day to say, look, this is today, today is Monday, that's a Mummy day.
Something that helped with the separation anxiety for me was always saying "Bye bye, back soon" when I left DS even if I was only going to the other room or something. I never left the room without telling him and as soon as I came back I'd say "Hi, I'm back" - just a simple word (back) that I hoped he'd associate with meaning I wasn't going away forever. I then used that when he went to his dad or to the childminder. I think it's also important not to do the pretending to leave without him thing - I know that it's really common and lots of people do it, but you're trying to reassure him at the moment that mummy/daddy aren't going anywhere and that if you leave you'll definitely be back for him, so I felt like the pretending "Bye, leaving you in the park foreeeeever!" thing was sort of undermining to that. Also I think it's good to talk to him and give him words. "You're sad to leave Mummy but you're happy to see Daddy. You have two feelings." And one more thing that my son loved was when I gave him "spare kisses" to put into his pocket and pull out if he felt like he missed me. Apparently he would carefully transfer them under his pillow when he went to sleep 
He was a little bit older at that point, though, but you could try it. And the same with something to remind him of Dad when he's with you. You could even make a little photo book with him about his two houses with pictures of each bedroom, what kind of duvet cover he has, what he normally has for breakfast at each house, how the routine differs and the fun stuff that he can do to make it into a sort of celebration of the fact he has two houses. If he can take his book with him to and from then he can always look at it if he feels a bit sad or homesick and it can help remind him of the routine and rhythm and that he's loved and secure in both places.
So onto general 2yo stuff. A lot of tantrums and silliness can be averted by silliness. If he's pretending he can't walk then start exaggerating some pretend concern. "Oh no! Are you turning into a wiggly worm?!" and act like you're really worried (in an obviously jokey way) and keep checking for signs of worminess, like if his feet are still ticklish. That can put them into a more fun mood and avert the tantrum. Giving him two choices which are both acceptable to you is useful. "Would you like to hold onto the pushchair or sit in it?" "Would you like to wear trainers, or wellies?" Avoid "Are you going to..." or "Do you want to sit in the buggy, then?" type suggestions as it just gives him a clear avenue for a NO!
Challenging him to a race is something DS used to love. Obviously you have to let him win And giving him a job to help with (especially if you pretend you're really rubbish and need his help) is a great one too. "Forget" how to put his socks on to make him laugh. Build in lots of extra time to do everything and slow down to his pace, and don't try to fit too many things into a day.
Good luck! I hope that things improve for you soon :)