Nepal govt does not recognize dual citizenship. So you might have to renounce your Nepali citizenship while you're in Nepal. Otherwise you can just get a visa from Nepalese embassy in your US passport and go to Nepal on that. The Nepalese embassy in Washington DC is pretty quick on giving visas. I think it's about $35 or so for a 30 day single entry visa. But I would not recommend your initial plan as TIA people will give you a lot of hassle. To solve that you either need be loaded (with some cash) or know some higher ranking officials who can make a phone call and threaten the TIA officials with their jobs.