This pony is old, and may be older than you were told too.
What are you wanting to do groundwork with her for?
She may well be past age when she wants to do much period, much less groundwork for no purpose.
Get a younger pony, or small horse would be my suggestion.
what you saying about older horses? XD mines 22 and loves jumping, hacks, hunting etc... have you never heard the say ' the more you treat a horse like its old, the more it acts like its old'? Aha
I still do groundwork and natural horsemanship with mine as it helps strengthen our bond as im talking in his language for a change instead of him having to try and understand me in a language he doesnt understand
Maybe try doing join up ( youtube it) to show who's the leader in the relationship might help with kicking issues.
I watched a tv programme which featured a girthy horse being 'cured' as such, and as I work at a riding school with lots of girthy and bitey horses, I tried out the technique with them and its helped a lot!
What you do is:
Get all the tack you need out and detach the girth from the saddle and the saddle pad from the saddle and set them out , tie the pony up close by
Start with the saddle pad, rub her with it then put on her, wait a few seconds, the take it of repeat until she shows not reaction to it ( could take awhile be patient!) repeat on other side
Do exactly the same with saddle till no reactions ( both sides of horse)
Then attach the girth to one side then remove repeat till no reactions (both sides)
THEN FINALLY do up girth then undo after a couple seconds, repeat till she doesnt care anymore the repeat on opposite side and then just leave it done up :)
Longwinded but it worked for mine who already bit when girthed, hopefully it will work out for you! :)