How unbalanced are you going in that direction?
Just as stated:
One last question, is this evident for all persons riding her? IF another rider doesn't have this issue, then it might be a crookedness in YOUR body.
I would stop and question your position and your body first and rule that out as a cause.
Just to add - your horse is 4
She is round and soft when she is going clockwise,
What do you mean by round?
She's also lazy, and very heavy on the front end and doesn't lift her shoulders so I think that is another reason she might be having problems.
She is 4! You as her rider and trainer, needs to take some steps back, and go back to working on relaxation and as loosie stated - trot poles, and hacking and focusing on basic level dressage. Rhythm, opening her up, allowing herself to track forward and move under herself, balance, strait, serptentines and getting her to lift her back up into your seat and getting her to use her body correctly. Do not worry about a headset!
As already stated, that will come on its' own accord when you are doing everything else right first. You need to make sure, you are using yourself correctly - because remember, our horses reflect 100% of what we are doing in the saddle.
If you have video footage of you riding, that would be very benefitial to beable to see what you are doing while in the tack, and to beable to see exactly what is going on to create the outcome you are getting.