That sounds really awful Op. 1 thing that stood out to me was yr sentence, sorry, can't c& p, along lines she moan, complains, argues, then it becomes an argument....' sounds like she's talking in a really negative way and you understandaly are getting drawn in and, well too much talking. Maybe have a chat and explain this behaviour is not on, it's negative and causes ill feeling all round and affects everyone and it has to stop. Then next time, After the moan, maybe try warning her, and if she continues she has to stop and or leave the room.
I got 1-2-3 Magic and i really loved this book. I recommend it. 1 thing that really struch me is the author saying we as paernts ( and possibly us women?) just talk too much, explaining, cjoling, responding to bad behaviour. And most of the time its too much, not necessary and even counter productive, as you've described, getting into arguments. Try breaking that cycle.
The 'you don't love me thing' sounds more like manipulation and trying emotional blackmail to make you feel guilty so you'll give in to her, rather than some genuine belief. I wouldn't stand for that either or respond to it.
Good luck. I'm having ( different ) fun and games with my 12 yr old, sil is having a nightmare with her 4 yr old. Kids, eh.