Then you have made a good discovery. If she secludes herself at home then she needs space. Give it to her. Stop trying to find things to do together at home, stop trying to work in the LL's right now and let her be.
That being said the way you behave with her at work should also change. You would not be discussing personal issues with any other co-worker so stop discussing personal issues AT WORK with your W. If you want her to not cake eat, don't let her. If she wants a change at home she needs to see there will be changes at work as well. It is not a pick and choose type deal.
You can do all this with a smile and a firm stance and none of it involves being an A-HOLE. You are very lenient with your W and her crappy behavior. Since you can't control how crappy she behaves stop giving her the opportunity to pick and choose when she acts decent to you. She has a reputation to uphold at work so it is easier to be decent and still lean on you in the office when it suits her. Are you okay with that?
