best sound with an ipad into my home stereo.

Well first of all I think you need a calendar. April Fool's was weeks ago.

Or if trolling then you need better bait. Because the answer to this one is simple- you get one of those ear jack to RCA adaptors and connect your RCA to your amp. Just like I do with my MB Pro. 

From there the next best sound is stick a Synergistic Research ECT on the iPad next to the out. 

is there a headphone outlet on the ipad?  If so then there ought to be a mini jack with RCA to fit it.  Don't know about balanced

Minijack to RCA. Forget balanced. Makes no sense because iPad does not have balanced audio circuitry. If you need balanced for physical connectivity purposes only get a RCA to balanced adapter.

No offense to previous posters but those suggestions are likely not the high quality connection that you are looking for.

What you probably want to do is get the advanced camera adapter kit from Apple. Depending on which version of the ipad you have, there are 2 different part numbers(both available on Amazon).

Basically what the "dongle" does is it plugs into the ipad where you presently charge it. The dongle will accept your power adapter AND has a usb output which pulls the digital feed through the ipad and out the dongle. Very easy, setup is virtually automatic. You then run the usb output to your dac(usb compatible) and into your preamp. This works pretty well, especially if your ipad is a Roon endpoint. This is what I use in my office system and it works very well. In the event you dont have a free usb port on your dac, a usb to spdif converter of medium quality will get you to be able to connect to your dac via spdif/rca. The Singxer unit will allow you to convert usb to any digital connection. Good luck.

I meant to add that if by balanced, you mean the balanced style digital connection to your dac, then the Singxer is what you want. Search Singxer or Kitsune.