It is US$83 for a 96-hour visa, which is quite expensive. Etihad partner with this firm to obtain visas, and it might be possible to apply online without the need to send in your passport.

That's a very long time to be stuck airside in an airport. I would advise you to familiarise yourself with the facilities available to you on the website: http://www.abudhabiairport.ae/english/

There is an airside transit hotel, located in Terminal 1. I have no idea how much it would cost, but the contact details are here. There are lounges in Terminal 1 that you can pay to access, but a stay is limited to 4 hours, and you would have to pay again for any additional 4-hour blocks. One costs US$39, the other US$50, payable when you arrive, and both are subject to availability of space.

A stay of 15 hours in any airport would be torture. You may decide the best thing is to get the visa and head out of the airport at least for a few hours.