Do what ever you feel is right, but if I were in your employer's situation I would wonder why you could continue your side job, which requires essentially the same functions of your primary job (sitting at a desk, talking on the phone, etc) but you were unable to perfom those same functions for your primary employer.
A doctor's note isn't a golden ticket, your employer can ask for a second opinion if nothing else. In the end, your employer may choose deny your FMLA (I would) and may either seek reimbursement from you or terminate you AND seek to recover the money.