Unsurprisingly given the circumstances, you've been respectful, patient, and forebearing, but it appears your dw is taking the piss advantage of your concern and consideration for her emotional welfare.
I'm sorry to say it's probable she's unburdening herself, so to speak, with another man and I suspect they've been doing considerably more than talking for the last 6 nights.
Sit your dw down and tell her that unless she is willing to re-engage in family life with you and the dc, she should look to live elsewhere while she 'sorts herself out'.
I have no doubt you'll make it clear to her that you are not necessarily expecting her to resume marital relations but, as it would be unreasonable for her to assume you're willing to live like a monk indefinitely, you trust she will seek counselling to resolve issues that should have been resolved many years ago in order that you can both embrace and enjoy the physical intimacy inherent in a loving relationship.
There's no need to be confrontational; simply state your case calmly and say that. after a full on 24/7 week with the dc unrelieved by her company, you're willing to take yourself down the pub or round to a friend for a few hours tonight/Saturday nght if she'd prefer to have some time alone with the dc, otherwise perhaps you can plan to watch a film together or organise some family activity.
No matter how hard you've tried to minimise/disguise/normalise it, their dm's frequent absence from the family home, coupled with your distress, won't have gone unnoticed by your dc and this state of affairs cannot be allowed to continue ad infinitum.
Given the seriousness of your eldest ds's problems, it's in his best interests for his dps to work together to bring about a positive outcome for him and, as the primary carer, you should seek external support if your dw is not willing, or feels unable, to give him the quality time and attention he needs.
I find it grossly unfair that you are under orders not to talk about these matters to anyone 'who may know us'. Do you have any close friends or family members you would feel able to unburden yourself to, and who you would trust to respect your confidences?