Some people make it work with cots and buttons together, but at other times the cots will suddenly turn aggressive and start pecking the buttons, so I wouldn't go that route. Besides, they are different species - where as they can keep each other company so they won't be too lonely, it's never going to be ideal. And a coturnix roo trying to mate with a button quail can't be pretty - it must be horrible for the button if he does it..
With regards to putting her with the pair, they'll probably try to kill her. Buttons are monogamous and in anything smaller than an aviary they are unlikely to accept a 2. hen.
I'd get another button for her. The sex doesn't really matter, so you can even get one that's too young to sex. Or just find a pet shop that has them and buy one that looks docile but healthy.
When putting the new one in with her, be aware she might not like it right away. Buttons are territorial, so whereas she wants someone to live with, she will likely consider the newcomer a threat at first and attack it. It might also be the other way round, and the newcomer attacks her, but that's more rare. In order to avoid attacks, keep them separated by a single layer of wire for a week or so - that way they can see each other and get used to each other without being able to hurt each other. Once you put them together, rearrange her cage to prevent her from being territorial.
