Not only has he cheated on and massively disrespected you, he's also cheated his children. He's shit all over your family and now he's been found out for the second time, he's shitting himself.
He's admitted that he's in love with someone else. im sorry OP but he doesn't love you, not enough to be faithful to you and your kids. Not enough to make the decision to not have an affair and not enough to stay away from this other woman. The fact that he was indiscreet enough that people knew that he was shagging about shows how little respect he has for you. He's not scared of losing you OP, he's scared of not seeing his kids every day and not having a cushy life where he has live in child care, gets to see his kids every day and then gets to shag his piece on the side. Can you really see yourself putting up with that for the rest of your life?
Also, what happens when he thinks he's off the hook and deletes the tracker app? What happens when he 'accidentally' leaves his phone at home? What happens when he does this again? How many chances does he get to have?
It may seem like an enormous mountain to climb, considering going on without him, but can you really consider living with him and knowing that he'll go back to her. Because he will. Or someone else.
He has no respect for you or your family life - if he did, he wouldn't have risked it by sniffing around someone else.
Eventually your dc will realise that something isn't right and it will skew how they view relationships forever.
Staying together for the children doesn't work as eventually the resentment will build and ruin it all anyway.
There's a famous saying: "fool me once, shame on you; fool me twice, shame on me" - don't allow him to fool you again, please OP. You deserve so much better and so do your children.