Welcome to Amanda!
DizzyN, everyone here knows what you mean about the sex. Even those who are managing anything resembling eroticism or fizzes of squelchy desire will admit that, overall, this is really, really difficult. I won't bore everyone again with the story of how long-term ttc destroyed my sexual relationship. Without a selfless DH who agreed to DIY artificial insemination I seriously do not believe I would be pregnant now.
I think you need to look seriously at your pattern of sex (or lack of) each month and say honestly to yourself: 'right, well, the nights out have to stop if they're going to clash with my fertile window.' You must, must must get the sperm in. It needn't be every night, but sex only once in your fertile window - especially if your DP's sperm doesn't last beyond 36/48 hrs - is never going to get you pregnant.
It's hugely frustrating to read of your missed opportunities month after month (i know you cannot help long shifts) when it is a fact that, even in our early thirties, only one in three eggs are capable of being fertilised.
That's why the consistency of the sex has to be there: getting it 'right' one month in a blue moon could be the difference between getting pregnant next year or the year after.
Personally I think your DP is doing you an enormous disservice. He already has a child. You don't. You matter and your dream of being a mum should matter to him more than anything else in his life right now, because that, in the end, is what will get you pregnant: a partner who will fuck you even when he's shattered and despite there being a dearth of 'filth' in your ttc sex lives.
Have a proper word with him, Dizzy 