Can't get on the same page with parenting...

We have been together 2 years. We are a blended family and our 4 kids are young, 4, 5, 6, and 10 years old.

He changes rules daily and I can't keep up. Like one day the younger ones wont be allowed a drink after 8 because they might pee the bed, they have before. The next, "they can have a swig of water because it wont fill there bladder". My issue is the kids dont understand amount just dads says yes mom says no. And now that's what they think because they will either wait til he gets home to do anything or tell on me (didn't know how else to word it) when he gets home "mom wont let me do this" or "mom made me sit in the corner" but he rarely takes my side. He thinks all 4 should receive the same punishment and most of the time it's just threatens with no action, "quiet down or you'll go in time out", "no running in the house" "I said not to, one more time and you're going to bed" when he's told them numerous times already but wont do anything. I dont think I punish unfairly but I dont believe the same punishment will work for each child. Like my 10 year old could care less about being in timeout but taking her game or books away or not allowing her to play outside will change her attitude. I allow my 10 year old to play outside or walk a few blocks to her cousins by herself (we live in a safe community and me and her cousins mom text when a child is heading over and when they have made it) which bf finds unfair sometimes. I either don't punish fairly, not enough, I favor one child over the next, or I let them get away with things. These are all told to me by my bf. I can't just discipline mine because then he'll give me crap about not treating his like my own. He says I love mine more and that it should be equal. My kids lost there dad very young and his kids mom just comes around for their birthday and sometimes Christmas. I have told him I wanted to break up before but he uses the kids situations to guilt me into staying saying things like "dont do this to my kids, your the only mom they have", "(my son) needs a father to teach him to be a man", "kids need 2 parents" etc. We were both raised by a single parent btw. I don't know what to do anymore.