The idea to take her to a chiropractor is good--they can realign the spine. It's amazing how many "issues" people have that can be cured or vastly relieved by a few adjustments. Not saying it will cure your daughter, but it might offer some relief, even if just temporary.
The other idea is to take your daughter to see a Naturopathic doctor. You said you want to find "the cause." That is what a naturopathic doctor does; he finds the cause of the problems and doesn't just put a Band-aid over it, which is what allopathic medicine does. Perhaps there are supplements or amino acids or even enzymes that she can take that would help with this issue. Most people don't have the right kind or enough of the different enzymes and amino acids the body (stomach, gut, everything connected with that, which includes the throat, since that is where digestion begins, after the mouth/chewing) needs to digest food properly. If that is the case with your daughter, then maybe there is something she can drink or eat (a supplement) before she eats her food that could help aid in the digestion process. Her body is lacking something it needs to break down her food in her mouth/chewing and/or on the way down the throat, which is why when the food reaches that particular spot of her throat/by her heart, it stops and gets stuck. For most people, the food would be digested well enough at that point from all the acids and such the body secretes that there isn't anything solid enough to get stuck there.
Another idea: have your daughter chew every fork/spoonful she puts into her mouth at least 30 times. Most people just shovel in the food and never take the time to properly chew the food so that the digestive juices have a chance to work on starting to dissolve the food. I currently see a naturopath for some issues myself, and that was one of the best pieces of advice I was given--to chew my food more thoroughly.
A naturopath will have the patience and the time to not only uncover what is causing your daughter's issue, but he'll take the time to help you figure out how to cure/handle it and give you tons of advice. I love visiting my naturopathic doctor, and I rarely ever go to see an allopathic doctor any more. I also haven't been sick the last three years--ever since I started seeing the naturopath and getting my body healed. Good luck!