The very first thing to consider is your experience. Do you have experience in safely working with a "hot and moody" horse? Do you have experience in safely working with a green broke horse?
There is this saying that goes something along the lines of: "Are you really "busy" or are you just figuring out your priorities?" Working with two (or multiple) horses is possible; many people do it, including me. You have to think about the long term effect or results of you working both horses, including one you do not own.
How long have you had your mare? She is green broke for a reason. Are you willing either put in a lot of time for both horses or possibly take away time from your mare? When a horse is, by your definition, "green broke", it is not a good time to be slacking off and be "neglecting" (training wise).
Horses that have "problems" have "problems" for a reason; your friend's mare has "problems" for a reason. Horses are usually a reflection of how they are handled. Even if you work out her "hot and moody", "bring her groundwork up to par", train her, and get her going good, it doesn't mean that the horse will stay that way and behave well with your friend, especially as you say she does not have a lot of experience with such horses. Although that is good experience for both you and the horse, it can also be a waste of time in the long run.
Summer only lasts for so long. What happens when you need to go back to school or work? What happens if you do not achieve your goals for your friend's horse?
Again, it can be done. There is no concrete, real advice or schedule as everyone's situation is a little different. It takes time, prioritization, determination, and hard work.
I will say that if you are short on time, do not take this other horse. I understand that you wish to do Gymkhana, and I am glad that you are taking your horse's opinion in that matter. However, if you are pressed for time, it is easy to try to take short-cuts, which cheat both horse and handler.
How is your relationship with your friend? People are often very passionate, as they should, about their horses. What happens if her mare gets injured while you work with her? Would she try to press charges? Should you take this other horse, get everything in writing. The horse world can be a dangerous place and liability is everywhere and that can be friendship ending.
"I hear and I forget. I see and I remember. I do and I understand." - Confucius
Last edited by LoonWatcher; 05-01-2019 at 02:16 PM.
Reason: Grammar. Adding.