Maybe too late for this since it's March, but........You can't get the stopover in CVG with United miles unless you're starting in HYD. Your free segment has to be in another zone besides the one you are originating and returning to. So you could book the return, HYD-CVG, then a free segment CGV to ORD, lastly a throwaway back intra-India (or book something you can use if you'll be back). But that's a lot of work for such a short free segment. In the old days of United awards you could have done what you want much easier, but no longer. San Diego was helping with the idea of a layover (less than 24 hours), which if the routing works (yours doesn't, as mentioned) can still sometimes show up. But your goal of a stopover (more than 24 hours) in CVG is not possible if starting in ORD.
As for options on airlines, I believe you're limited because Star Alliance has only Air India and Thai flying into HYD. It's not easy to force connections anymore, but if you can stop in DEL or BOM, and then buy a cheap ticket to HYD, you can get many more options, like Swiss, Lufthansa, or ANA. In theory you could still get those long hauls, then a short connection on Air India, but unfortunately I'm not aware of any ways to force those flights to appear in the search since I burned my United miles long ago. But you might play with multi-city or time of day or something and see what you can get. Good luck.
