The way I see it... your kids are going to figure it out sooner or later, and they'll spill the beans to your dad soon thereafter. I highly advise against asking them to keep it a secret because that attitude breeds all kinds of shame. In other words, your dad's going to find out eventually, and it would be better for him to hear it from you, the way you want him to hear it, rather than vague and misunderstood the way his grandkids might tell it. If it comes from them, he'll probably assume you're cheating. Even though cheating is more acceptable in our ass-backwards society, it's not likely to win you any brownie points.
I don't need labels to define me. They're sticky and I hate the glue they leave behind.