Should I take my mom back home to get her things when she can't return home for good after a hospital stay?

My mother has Alzheimer's and is 83. She's been able to remain in her home (with frequent visits from us) until last week. She had a series of falls (wasn't hurt), most likely caused by a UTI. After a trip to the ER, we brought her to our house and told her that at least until the infection was cleared up and we felt sure she wouldn't fall again, she'd be staying with us. A few days later, she was admitted to the hospital because the infection worsened. She's going to have a couple weeks of rehab to help build her strength, but we feel like she shouldn't return to her home. The professionals agree. My question is: do we take her back to her house to pick out those things she wants to bring or do we prepare a place for her while she's in rehab? I want to give her as much control as we can, but I'm also afraid that it will be too hard for her emotionally to go back there. I'd love expert advice as well as to hear about the experiences of others who have gone through a similar circumstance.