Alpha Thalassemia and anticoagulant

My 25 year old daughter recently suffered DVT as result of a femoral catheter.  tPa removed 100% of the clot and a filter was placed just below her sternum (to be in place for a period of 3 months to a year).  The Dr. is attempting to raise her INR levels to the "Norm" of 2-3.  After interveneous heparin and altaphase for 4 days and another 4 days of lovonox  (2x daily)and Coumadin (10mg) her INR is just 1.5.

I understand that conventional DVT treatment to raise INR to therpeutic levels is generally 3 to 5 days.   Without a baseline what would be the rational to attempt to raise her INR levels to the Norm".

It is the bodies natural defense to clot when cut.  Why would a lifetime  Coumadin therapy be reasonably perscribed after experiencing DVT related to a surgical procedure?