Has he always found it 'hard to relax in general' and was your friend aware of this before they married?
On the face of it, it sounds as if he has a demanding job but he's not thriving on its challenges and is bringing the stress and pressures of his work home with him.
In the absence of specific examples of his behaviour, I'm inclined to the view that he's neither emotionally abusive or depressed but he is in need of strategies which will enable him to switch off the work button and turn on the dh/df button when he's at home in order to promote and prolong his physical and mental health.
From what you've said, his dw is understandably frustrated with him and I suspect she's also royally pissed rightly peeved at having to parent their dts and most probably undertake the bulk of the grunt stuff while he swans around being moody and anti-social. < miserable git emoticon >
There are numerous internet sites dedicated to helping men beat stress by learning how to separate work from play and this book www.amazon.co.uk/Beat-Stress-Better-Steve-Baxter/dp/1906121869 together with the the Men's Health Forum website may be of interest to your friend.
With regard to their relationship, as I'm not a great fan of Relate I would suggest she sources a local couples counselling service through word of mouth recommendation if possible so that the pair of them can discuss their differences/expectatons of each other in a structured setting as rows discussions of such matters have been known to cause negativity to seep into the marriage bed woodwork where it casts it pall over the whole household.
If he responds with 'I'm too busy to attend weekly/monthly sessions', I would suggest she makes it clear that if he can't find the time to save their marriage from the brink he can go live at his place of work.
If he's continuing to 'find fatherhood especially challenging' there'll be a course for that too 