My mother is 91 requires anti-coagulants, need second medical opinion?

My mother is 91 and lives in Aged Care. She is wheelchair bound and cannot walk by herself at all. Two days ago a locum advised that she has Cellulitis in her leg and started her on a course of antibiotics. Today her regular doctor advised that he thinks it might be DVT instead as the swelling goes from her groin to her ankle. He advised that we could do a test to check if it is DVT but there is no point if we are not prepared to put her on anti-coagulants. I have done some googling and there seems to be differing opinions about giving anti-coagulants to the elderly. I am looking for a second opinion as this is a very difficult decision for me to make.