You can likely run the coax that far and the picture quality be just fine, with no issues that you will notice; you can always add a small amplifier, if necessary.
If she is going to have her own receiver, then you'll likely need to upgrade your LNB (coax connectors on the Dish, itself) to a triple LNB...although I have tinkered around and have split the coax and used two receivers with it...so I don't know what to tell you. I would recommend the upgrade.
DirecTV will likely install this for you, for free...if you ask, since you'll be adding more service - but I understand if you are trying to avoid the DirecTV route, due to this receiver being at a "different address" than your account.
Lots of new, cheap dishes out there that you can replace your current on with, that will do the job: [
search.ebay.com]
...in fact, I'm thinking about upgrading mine (for HD) - so I might buy one. lol