The person is simply trying to provide the best care for the pets by suggesting a stay-in arrangement, minimizing the animals' time alone. It's a more practical solution than driving back and forth multiple times a day. Given the sister-in-law's OCD, the person has always been careful to maintain the house's order. The sister-in-law is being unreasonable.
It seems like the sitter is prioritizing their convenience over the sister-in-law's mental health and comfort in her own home. While caring for the pets is important, respecting the homeowner's boundaries and anxieties should take precedence. The sitter is downplaying the sister-in-law's OCD and making it all about their own inconvenience.
Staying at the house would reduce the pet's alone time, but the sister-in-law's discomfort is also a valid concern. The person has a history of respecting the house's order, which mitigates some concerns. However, the sister-in-law's mental health should be considered. If the sister-in-law's anxiety is severe, her feelings should be prioritized.