"I want to sincerely apologize to the Romney family if anyone was offended by my joke" is not an apology. It puts the burden on the offended party. Yes, I was offended by your joke, so now will you apologize? How about offering a sincere unconditional apology, something like, "What I said was offensive and wrong. I am very sorry I said it, I apologize and I hope the Romney family will accept my apology."