Obviously I've been looking too much at Tekes lately.  Because I'm not thrilled with her , and I really strongly dislike her sire. STRONGLY! 

She's not as bad, but I would worry about all the riding she has been getting, what with the combination of bad feet and angles and matchstick legs (relative to body mass).

That is a lot of riding for a 3yo, so good that they are not loping her.  I'm guessing she is having issues and that is why she refuses to lope.  Even the most pluggy horse will shamble into a lope (IME), but not stay in it very long.  If she is refusing to pick it up... think twice.  Obviously could be having balence issues, as will do it on the line, but not under saddle.  Or even pain with the extra weight under saddle?

Most of her issues sound like holes in her training.  Like she was rushed.

So, maybe if you restart her training (and fix her poor feet), take it slow, she will turn out really nice for you.