Haha, sounds like you're doing a horse clean-up just like I have. I've been trying to get weight OFF mine though.
I think she looks pretty good in the last few pictures. She doesn't look badly underweight. I like my horses on the chunkier end of a healthy weight, and she'll probably put a little more on as the richer grass comes through anyway. She looks pretty good though. If you don't mind me asking, what was going on with the scarring on her shoulders in the earlier pics? rug rubbed or something?
I'm not one to give much advice on training, although well done on getting her home calmly! As for the coughing, My mare is a cougher. it could be caused by a weak respiratory system, and is often aggrivated by dust. Especially if the ground is quite dry where you are. You can get supplements to put in her feed that should help it. My local tack shop has several things available. My mare is one one called respirator-boost which seems to be working well. Although I've seen others. Maybe you could find one suitable for her?
~The most important lesson my horse ever taught me is how much I have left to learn~