Hello,
I'm very sorry to hear about your daughters current diagnoses. I also had TOS(paget-schroetter syndrome) clot removal surgery and 1st rib resection all within a 2 month period. I personally would recommend having the rib removal surgery but only by a Vascular Surgeon who is familiar with TOS and has performed a rib removal at least 20 times or so. Also keep in mind that some doctors are trained to go in directly above the Clavicle while others are trained to remove the rib from making the incision below the arm-pit( my doc went above the clavicle and it turned out fine). As far fetched as it might be Stanford has a great staff (Dr. Jason Lee) and would be ideal if you could make it out here.
Once the rib was removed I had some lymphatic fluid swelling in my shoulder which resulted in referred pain in my back but all in all I'm glad I had the surgery. It has really helped put my mind at ease knowing that I'm not going to cause another clot next time I reach up high or extend my arm out. Here is a verse that helped me .Deuteronomy 31:6

I wish you the best of luck and will keep you in my prayers.