If you use the right home upgrades, a girl will remain with you at your home without ever needing the care home or the facility. They're an alternative gaining route past immobility for girls who don't live with you, or if you don't get the larger bed upgrades in time.
Your best bet might be to fatten up another girl. If you have the Dizzy's shop open & staffed, your employees are good options as they'll passively gain from Dizzy's addiction, plus you can work on the shop floor for workplace fattening shenanigans!