I need a push.. pls help

So I feel my relationship might b over. I'm not happy rt now. He's not happy. N to make things worse it's affecting my parenting time.. My job.. I hate giving up on us. I feel like it's letting the other dwn. I drive him nuts bout a few things. He drives me nuts about a few things. He verbally abusive but somehow it's my fault.. He's not really there for me. He likes to b a shoulder to cry on (as long as the problem isn't something he's suppose to help or fix n as long as my head doesn't block the view of the tv..seriously) my biggest issue is I don't kno who he is sometimes or if I can trust him. He lies about stupid shit!! He volunteers useless info "I never go outside n stand w joe when he's smoking" ... I'll call n he answers n says sorry it took so long I was outside w joe while he's smoking. N I call him on it. Because he made such a huge deal out of saying he didn't. It's WEIRD rt? Y point it out if ur not hiding anything. He says so what I wasn't doing anything wrong. (Joe is a womanizer n is crude about women.. but my guy claims to b polar opp) so his excuse is well I'm not doing it. They r around me.. y have so many friends that r this way if ur not?? Also he says who cares I'm not doing anything wrong. Well ladies I'd assume he's doing nothing wrong. But he makes a point to say things n does other stuff.. little stupid things like this. So since he's making a point to say stuff n doing others.. it feels like a red flag? What r ur thots? Am I nuts to question his intentions? Or do u need other details. FYI. This guy did cheat on his wife but as usual it was her fault. She wasn't satisfying him... 
Y I GOT W HIM: 
I was dating a guy who made good money n stable (boring) never wanted sex.. left him. n this guy currently w came around n made me feel so important. Gave me his time. Which meant more to me than money. He smothered w almost w it but I hadn't had that in so long I loved it. He was high sexual appetite like me.. he presented himself as morally sound. Family oriented n very dedicated to sexual satisfaction of his partner. He maintained this for bout a yr or so.. then drinking started. Then by family he meant drinking w alcoholic family late hours. Ditching kids to do so.. sex on back burner. He's either alcoholic or bipolar. Maybe both.. moods swing all over.