I don't think you are abusing her, but I understand where you and her sister could worry about that. Because IMO it sounds close to it, or like it could develop into it.

Do you put her down or try to make her feel bad about herself? Do you want to punish her for her lies?

It's reasonable for you to talk about your feelings and say "if X happens, I don't think I can stay with you". Saying "do X or it's over" is a little different, it's not helpful, but it's still not abuse. BUT saying something like "if you do X you're a bad person/not good enough for me" IMO is abusive. saying "we might have to talk about you moving out" is reasonable. saying "if X happens, I will throw all your shit on the lawn" is not. do you kind of see what I mean?

I lied to my parents while in high school about my grades because I was afraid of their judgment. They were in no way abusive or close to it at all- I was just very insecure and afraid to disappoint them. I've also been in abusive relationship where I lied to avoid conflict and abuse. I was in the wrong, but I couldn't hear to stand the things he said about me. (I won't go into details, but it was much worse than what you describe here.)

I'll ask you this: What is the purpose of these "arguments"? If you're just yelling at her while she's crying, what does anyone get out of that? You are just venting your anger, and hurting her. She knows how you feel, right? It's not like telling her again, louder, is going to make a difference. Don't feel like yelling or cussing or ANYTHING is going to get it through to her. SHE KNOWS. You need to think about why she acts this way, whether she wants to change, and whether you can deal with the situation. Maybe you can't, and you do need to split up. THAT'S OK. It's not the end of the world. There are so many things that are worse than a breakup... and a horrible relationship where you resent her and she's afraid of you is one of those things.