I think that getting at least a little time to recharge is vital! If you & DH are both home in the evenings, you could schedule in 15-30mins to have time alone after work. DH is on duty and no one should disturb you. Lock yourself in your car with a book if you have to, or stop somewhere for a bit on your way home from work. I need way more time to recharge than some other moms seem to. It has to happen on a daily basis. If I don't get that time, it's really really hard to stay calm & present. And once a week or so, I need a longer stretch of time, several hours straight. And DH and I try to communicate/trade off duty whenever he's home -- I'm willing to cook dinner as long as he can entertain DS... or he can cook while DS & I do something together. It's stressful to try to cook and entertain DS at the same time, especially if I'm really hungry or overtired.
How much time do you spend reconnecting with your DD each day? Is there an activity you particularly enjoy doing with her, that you could do on a daily basis? I hate playing, but I enjoy taking walks, doing crafts, reading, going places, talking, etc. with DS. It sounds like you & DD could both benefit from having some special time together on a regular basis, just doing fun things & enjoying each others' company. Choose something that won't feel like a chore or a burden to you, share your own hobbies & interests with her. If all your interactions with her feel like conflicts than you need to balance that out with fun time where conflicts aren't likely to arise.
Can you make your rules & expectations clearer? Like for TV time -- can you just set up a rule about it so it's not a negotiation? Or give her X coins/tickets a day to turn in for TV, and when she's out of coins she's done with TV? Also, can you think up some ways to make the points of conflict more fun, make them into games or something? The book Playful Parenting (by Larry Cohen) can help with ideas of how to make this happen. I help DS get dressed (even though he doesn't actually need help, at least not physically, but it goes smoother if I'm there) and we pretend things like I am the zookeeper and I'm brushing him & feeding him, or he is a bear and needs to put on his fur (aka his clothes) to stay warm (he loves to pretend he's an animal). Picking up toys can be more fun by making it into a race with you or singing songs together while you do it.
I'm glad your DH is supportive. Lean on him! Let him bail you out. And bail him out in turn.