You are being your own worst enemy. Get him out of the flat, TODAY, NOW! The reason? he is shagging someone else, underneath your very nose and has not stopped. HE left, he needs to STAY left.
You will never, ever, EVER in a million years regain your dignity and any shade of respect while you allow this situation to carry on. Currently what is the incentive for him to behave better towards you? What's in it for him to change? NOTHING!
You are allowing him a roof over his head, a roof HE left you in with your DT, to go off and shag someone else, and now you are allowing him 2 nights a week and now you are popping back for more abuse, contempt and vitriol.
How long before you just move back in permanently and he carries on fucking anything that looks at him and you just resign yourself to a life like that? Jesus, It doesn't have to be like this!
Five years is 5 years. I was with mine for 10. Does that mean I'm less of a human being for telling him to get the fuck out of my life as he refused to stop abusing me? Does that mean I have had less or more return on my 'investment'? No it doesn't. It actually means that I was ALMIGHTY prick, and that I am going to take a lot longer to put myself back together than you. I may never recover.
It's no different whether you have been with someone 5 years or 50 years, if they are mistreating you, disrespecting you or lying to you, the length of time means nothing, it can't change the facts.
If you are looking at this as an investment, tell me what return are you actually getting out of this? To be in a relationship at ALL costs? Nothing, no-body and no dick is worth that. Believe me.
What do you think this all will show your dear little twins? To grow up and be cheated on by someone who is really not worth it?
Surely the best thing to do is to cut that man dead and tell him that when he becomes a human being, does the right thing then he can be treated as such.
He HAS, as you say "fucked your head completely to make you doubt your own instincts to the point of such self doubt and the feeling of going mad."
So given that statement, can we please establish that
ONE, he is not to be engaged with,
TWO, that he doesn't have your best interests at heart, far from it,
THREE that he is using manipulative and abusive tactics to control you
FOUR you are miserable, confused and panicking... all of which HE is causing by his refusal to treat the mother of his children with the respect and consideration she has damned well earned and truly deserves.
You are not IN LOVE with HIM. You are in love with the person he tricked you into thinking he was. He is not that person, probably never was. Of course he has been semi nice to you, a smile here, a there-there, erm, there
but that is part of the cycle, You are addicted to the snippets of nice that he tosses you every so often.
OK, tough love over, I want you to be happy, carrying on in this day to day self flagellation trip will only break you. You need to find some strength and boot that fucker as far as your eyes can see, and then boot him again, ideally behind the sun.