FFS, this man's wife is exhausted - this has been relayed to him time and again but he still keeps nagging, and pestering, and sniping at her. Which of course, are all well known seduction techniques aren't they ? 
If he had an iota of intelligence and if indeed he "clearly" loves and fancies his wife as a person (compared to a convenient source of sexual release) you might think he'd consider how he could alleviate her exhaustion first and foremost. You might think he'd look honestly at how much work she does in the house compared to him, you might think he'd look honestly at how much time she gets to sit down and/or do her own thing compared to him etc etc etc., and seeing as they're both working FT, do whatever's necessary so that they both share an equal burden in regard to all that has to be done within a household. If he can honestly say that he's sharing all the drudgework 50:50 then the next step would be to start to get worried about his wife's exhaustion and suggest - with sensitivity - that she ought to see her GP just in case of any underlying physical or indeed mental cause.
Only when he's done all of that would he perhaps be "justified" in feeling hard done by and "rejected" when it comes to sex. And do you know, a man who "clearly" loved his wife still wouldn't attempt to "seduce" her with unpleasantries but would speak to her calmly about it - and not in the middle of trying to get his leg over - e.g. is there anything worrying her which could be affecting her libido, is there anything he's inadvertently done to upset her, is this something she and him could work on together, is there anything he can do better/differently to help get her in the mood, would she consider sex therapy and so on and so on.
Quite apart from all else, "joking" about men who cheat on their wives - when he's having sex twice a month anyway - and when, so far as we've been told, he's making no other effort to reduce his wife's exhaustion and/or make her feel better generally and/or show her that he loves and respects her as an individual (instead of a convenience) - is just plain mean. It's small wonder OP doesn't feel filled with enthusiasm at the idea of sex with him. And yes, this will just fester, because she will feel more and more resentful at being treated like an object.
Maybe if OP laid it all on the line to her DH about how she feels and what he could do to make her feel better and thus increase the chance of their sex life getting back on a more mutually agreeable track he'd have a sudden revelation about what a boor he's been but I wouldn't hold my breath (obviously it'd be good if he did). I suspect he's more the sort who'll feel even more hard done by because she's pointed out that he's basically been unfair and has been taking advantage of her - he may well even feel resentful that she wants him to do more "women's work" (housework and childcare) in his eyes. He would probably run the hoover round a bit more and then think he's done his bit. The ONLY way this is going to get sorted is if OP and her DH are both totally honest about the WHOLE picture and work out a way forward where neither feels totally exhausted. He also needs to understand that things change with kids - even if he was sharing work and responsibility properly - you are still likely to feel more tired than you once did and it's therefore not unusual or unreasonable to want less sex. He can help create optimal conditions for sex, but sex should never be an entitlement as such and he needs to accept it still might not be exactly all he wants. That's what his hand is for.