You're blaming your relative for choosing to stay in your marriage when you first had doubts. That was crap advice and you knew it then just as you know it now. You didn't stay because of what that person said, but because it suited you to stay and you didn't have the courage to leave.
If your affair is discovered then that has an equal (if not higher) chance of scarring the children and the two families as a divorce. Yet again you must have known that logically, but you thought it was worth the risk.
If the OM is now distant and has ended his other relationship, chances are he has met someone else. Not unusual behaviour in someone who was having an affair with a married woman while in a relationship himself. The distance is unlikely to be associated with impatience and even if there's an outside chance that you're right about that, he has no right to be issuing deadlines when he's only just dumped his own partner at christmas and you're dealing with the final stages of a loved one's illness.
I don't quite get your or your counsellor's logic that you don't love your husband as you were faithful before. Why are the two things so linked? Maybe you haven't loved him for years and your previous fidelity proved nothing more than you didn't have the opportunity to be unfaithful? Or maybe you can't bring yourself to believe it's possible for you personally to love your husband and be unfaithful and have feelings for another man?
If I were you I'd deal with the family issue first and if it would really pour salt into open wounds if your marriage broke up now when the families are anticipating bereavement, wait it out. If the OM has scarpered by then, there's a chance you'll see your marriage and feelings for your husband more clearly without this interference. I'd be very surprised if your marriage hasn't got even worse as a result of this affair, but that's not to say it wasn't bad before it started. So if the marriage is beyond help after the waiting period, make a clean break of it.
Be honest wth yourself though about why you stayed before and why you're staying now. It's so unlikely to be solely because of what the family member said or because someone's dying now. A lot of it's likely to be your own fear of what you stand to lose if you jump ship.