You're going out of your way to prove her that you don't care about her, but she's just rubbing her hands together like "there you go - he IS obsessed with me".

... доказывая...

From an English point of view, I don’t understand the gesture of rubbing your hands together.

Uly, it's something like "I got you!" or "I'm gonna get you anyway"
Though you are saying you dont care, I know you are mine!

Another example, perhaps too literal, but imaging you are hungry and barbecuing a duck slowly. After an hour or so the duck is ready. Now you are rubbing your hands together anticipating how you gonna eat it in a minute or so.

Oh, you mean like when you hold your hands in a praying position 🙏 and move them up and down against each alternately?

How very interesting! I actually made this up to see whether "rubbing your hands works" or not.
https://idioms.thefreedictionary.com/rub+one%27s+hands

Saying она только руки потирает they mean that he's playing into her hands when trying to prove otherwise.

If I was writing that, I would add something to make it clear: rubbing her hands together with a sinister smirk.

We also call this the evil hands: https://tenor.com/search/evil-hand-rub-gifs

Yes, Uly, you understood correctly - holding hands together as in praying and moving then alternatively up and down or back and forth.
As for Tatiana's "trying to prove otherwise" it's not necessarily. Doesn't have to be "otherwise". It's usually - "I'm gonna get you" OR "I got you, baby".

And there’s an evil laugh that goes along with it - mwahahaha! -or- bahahaha! https://www.lexico.com/en/definition/mwahahaha

The evil hands - exactly! Solved.

Osatio’s “translation” threw me off. I wish (s)he would remove it! It’s too simplistic.

Their translation is just my comment they copied, edited and pasted.)

Is that’s clever! 😡

Чем бы дитя ни тешилось, лишь бы не плакало)))))

Uly, спасибо большое за перевод! 🙏

Russ, я могла неправильно использовать prove otherwise, но я всего лишь имела в виду, что чем больше он старается доказать, что она ему безразлична, тем больше он фактически доказывает обратное. 😔

Tatiana, your PROVE OTHERWISE made absolutely perfect sense in your statement and especially in reference to this post.

Большое спасибо, Uly! Для меня это очень важно. 🙏🙏🙏