As Kiddo suggested, you definitely need to grow a pair. You need to decide what you want in life. After all that has happened and you know for sure that she is a dishonest and disloyal lowlife (note no offensive words), why you still offered to deposit money into her father's account is beyond me. You are either really stupid or learned pretty much everything from 70s and 80s cheesy Bollywood flicks. Regardless of that, you really need to take a pause and say WTF. As long as you act like a pussy, she will take every advantage of that. So stop being a pussy first. It is clearer than the dayfkinglight that she wants to push you around. Legally, I don't think you owe her anything. However, being such a nice guy you are, if you want to hand over your entire life's earnings and end up like a loser, be my guest.
1. Nepal's family law clearly states that if the wife is infidel to the marriage, then she does not get any property. If you have evidence of her admitting to this, you don't owe her anything legally. Instead you can claim wedding expenses from the guy who she fooled around with. If you consult a lawyer in Nepal, you will find this out right away.
2. She could have claimed your assets in the US, but it will be very difficult for her to prove anything existing in the US. Due to her cheating, she will be ineligible to claim anything.
3. You should stop ignoring her existence. Don't reply to her emails and just break contact. Ask to her to correspond with your lawyer about anything she has to say.
4. Proceed with the divorce proceedings in Nepal, but get a good lawyer first.
5. Once again, do yourself a favour and stop being such a pussy...