@dumpling12 I don’t think there can really be a rule book for things like this. It doesn’t matter if you read 50 articles that say it takes five years for things to return to normal. The question is: do YOU want to give it five years? It sounds like you’re stuck in this strange in between land.
With respect to what @Wisteriaroundthedoor is saying, my point about you not having sexual security with your partner is very much about WHY you can’t have sex now. You didn’t have a very intimate relationship before the affair, Wisteria is correct, but now you’re afraid that may have played a part in your husband having an affair and you also don’t feel secure in him being attracted to you because of the comments he’s made about the OW… so I don’t know if this will be fixed in a year or five years or ever. You didn’t have that security before the affair is the point, or you would have been having sex regularly. If you had felt loved/wanted/like your husband thought you were the sexiest thing on two legs, you wouldn’t have been having sex so irregularly before the affair, and as a result, it wouldn’t be so hard to “believe” him now when he tells you that he wants to continue being sexually monogamous with you, for the rest of your lives.
I’m just afraid you’re going to always feel like this, always be waiting for the other shoe to drop, or blame yourself because you didn’t “restart” the sexual relationship, when really, this is about more than sex - this is about how he treated the intimate side of your relationship before the affair, him having an affair, and how committed he seems to getting the intimate side of it back on track. If you do want to repair the entire relationship, and ensure he either doesn’t have another affair or ends the relationship before ever doing that to you again, I really recommend counseling. If he’s willing to beg and apologize and do anything, then he should be willing to go to counseling to see if this can be saved. All issues are, at heart, communication issues (EXCEPT abuse) and this is, too, in some ways - the way he’s communicated with you about the OW, the way you’re unable to communicate with him about your fears surrounding sex - and I hope, if you really do want to continue the relationship, maybe counseling can help.
If counseling isn’t an option, then please think about what YOU want. As for whether he’ll have another affair, because you seem terrified of that, I’m truly sorry, OP - none of us can tell you. In the past, I’ve thought that if a man had an OW that offered him everything (said if he left his family, they could live together, get married, start a life - so in essence, he had a whole set-up with the OW just ready to walk into) and he still ended the affair, then he was less likely to have another affair. But I’ve recently seen, even that’s not the case. There is just no perfect predictor. The best way is to communicate, with the help of a counselor if you need to, that cheating again is not something the family unit will survive, if that’s what he wants - the survival of you four as a single family unit. That you will respect him more, as a person and a father, if he decides he can’t keep his commitments to you, if he ends the marriage at that point. It will be better for the kids, your long term communication as co-parents, and your self-esteem as a person. But ultimately, if he WANTS to cheat, and thinks he can get away with it, and has nothing to lose, you won’t stop him.