As the grown up child of parents who likely stayed together, up to the breaking point, "for the kids," I recommend not staying "for the kids". If your relationship is strained, painful, unhappy..., that's no good for the kids: take my word for it.
Others say it all comes down to whether trust can be established / reestablished, and that's largely true -- but trust alone isn't enough. There has to be genuine loving, which obviously involves trust importantly.
Polyamory can be a good thing, I believe. And sometimes people can transition from deceit and cheating ... followed by honesty about deceit and cheating... and into some sort of happy poly situation, but, as others here have said, there's no covering up that you got treated badly by being lied to and cheated on. So the ball is mostly in *her* court, I think, in terms of taking responsibility for f-ing up and trying to set it right.
If you both can look into each other's eyes and say, "I love you and want this to work out; and I'm willing to work to be sure that it does," I'd give you good odds. If things are beyond that point, never mind the kids. They'd be better off with happy divorced parents than unhappily married ones.