I can only offer my view on this so please take it with a pinch of salt.
If he is actively pursuing other relationships then you might want to consider LRT, but for me this is a boundary issue as in you wont listen to him talking about it or conducting that sort of behaviour from your house.
Can I ask how you know about what he is doing? currently my W denies other man (not true and i know this but cant challenge her on it) but as she says, our Marriage is over, she is moving on and its none of my business who she dates and that I need to move on also.
Does it do me any good to ask about it? nope (i still do though which i know is wrong). Do i gain by talking about him? again no. Can me, our history the problems my W sees really compete with new relationship lust? again no and to try and compete with him and it does me no favours to try, i just look needy and i'm never going to win.
Now if I take this ^^^^ as true, that our marriage is 100% done and i just need to move on then for me the second best scenario is that OM is a really decent guy and that he makes my wife happy and will be a good step father to my kids and that we can establish an effective and postive coparenting relationship for our kids. That changes how I should interact with my wife, certainly is punishing or controlling her going to do me any good? probably not
Instead for me its about trying to be detached and get on with my life, improving myself and hoping that she has some doubts. She is much more likely to see the improvements if she is in the same house, whether she believes them or feels the loss is a different matter. when she moves out she has no need to pay any attention to me (we will barely see or speak to each other)
what this all means for you depends on where you are emotionally on all of this. if the best way for you to move on is to ask him to leave and then drop to minimal contact then maybe thats what you should do. If you can be in the same house, be positive yet detached with an exciting and mysterious life then that might be better. Only you know whats right for you
In relation to the sex starved side of it i have a couple of questions but dont want to intrude to much
Both mid 30s, 2 young kids BD 7sep14 XW moved on long ago, now living with OM1 D paperwork in progress