What's the difference between lovenox and coumadin?

I had gastric bypass surgery in 2006. Due to major weight loss (134lbs) I have a lot of excess skin which causes me to suffer from recurring boils and it's a major blow to my self esteem. I had a major stroke at 32 yrs old due to a blood clot in my carotid artery,my hematologist says that I have to take coumadin for life. I want to have a tummy tuck but the surgeon requires me to stop coumadin for 2 months 1 month pre-op and 1 month post op