You don't say whether your partner is a man or a woman, so I'll just say "partner".
I think your partner is incredibly picky and nasty. I leave lights on during the day - the cost of a lighting is miniscule compared to air conditioning/heating and water heating and cooking.
We leave the bathmat on the floor all the time. It's a part of the bathroom, the mat on the floor.
I think I would pull my hair out if someone in my household was so wrapped around the axle about nothing.
I say, lay down the laws that he/she quit making a mountain out of nothing, or move out. Your daughters don't need this misery.
I think you need to tell both of your daughters to have a little respect. Give them a power and light bill to look at. Explain how much you/your husband has to work to pay for that. And being lazy is a terrible thing to be. I hope you don't want your daughters to go out on their own and be slobs. I'm not saying that they are however I would NEVER have gotten away with that kind of behavior as a child. My 5 yr old knows better than to do those things. I don't nag him at all durring the day. He was taught and he enjoys a clean and clutter free home. I agree with your husband on this one. Good luck to you.
I would ditch the partner and then fix the respect problems at home.
I'm not sure if this will help but I can give you some imput..
My mother was dating this guy for a really long time (they are not married) and I HATED HIM.. he would nag to me about lights, about leaving the tv on too long, about leaving my shoes out in the front foyer.. all that stuff.. we would FIGHT constantly about it and I know we ended putting stress on my mother more than anything..
One night my mom came into my room (this was when i was 16) and she sat me down and told me how this is bothering her alot and how she doesnt know what to do...
I love my mother very much and even though I hated this guy she told me he was very good to her, and I didnt want her to loose that because I was lazy... I just didnt understand that they are paying all the bills and doing all that stuff, and Im just living there and I should respect them a little more.
So... I tried my best to just keep out of his way.. I just left the lights off and put away my shoes and would turn off the tv when I wasn't watching it... he eventually calmed down a little bit, I am 23 now and I still live with the both of them.. Him and I dont talk to much, but he slowed down the nagging, because my mother spoke to him as well... it's hard for a daughter to accept that this is not her father and thinking that "her father would never do that, or act like that."
I think what you need to do is talk to both parties and ask them to respect YOU if they can't respect one another or understand one another.
If they both love you enough, they will understand.. because this can be a HUGE problem if it's not handled soon..
Hope this helped a little bit.
Cheers