are the 4x4 posts set into the ground? if not those corner braces are not enough to provide anti-racking stability. you will need 45 degree corner braces on each corner. going 2x4 on the floor joists did not improve the situation. but may be adequate for youth sized occupants. I am guessing you are getting side to side wobble without the braces, and up and down wobble from the 2x4's.
the floor could be strengthened by adding additional joists in between the existing. I would put no less than 3/4" ply on the floor. or 2x6 deck boards would stiffen it up.