Thank you. I hate the design. It wasn't what I asked for at all. It has been a nightmare. I was hoping something could be done to at least make it presentable. But it feels (when I run my hand across it) like where the seams of wood come together it is unlevel.

Can we get a better picture standing back. I have an idea that may help fix your issue, but I need to see if from a distance.

Prep is the key to a good paint job and the painters did not do a good job. I'm not sure they even sanded. Sophie is correct that MDF, MDRF, or even MDO are much better substrates than wood but I can see the vertical joints and nail holes even from far away. I think yo may need to repaint.

Couple of more questions, is this buckling at every junction or just these two junctions? The problem is the wainscoting was not properly constructed. You don't use wood strips between pieces of plywood as a method of joining the pieces. If you are in an area with wild humidity swings you would do some sort of tongue and grove or other method to join the pieces of wood together so they don't torc. Wood that is butted up like that will never ever lay flat. You have two choices - try to fix it or rip it out and redo it. You can try the repair, but my opinion is it will come back and you are just wasting your time. The other is to finish the room and realize that when everything is in it no one but you will likely notice the defect. If you go into old houses they always have things like this and people call it character. Enjoy your home.