I am also in NY and my insurance agent just dropped the business liability (and almost my homeowner's, had a certain time frame to get separate insurance) so I would call and ask IF you got separate liability insurance would they still cover the house, and then go from there.
I went with
https://assurechildcare.hayscompanies.com/
If not, I would call a TON of agents to get quotes on both coverages. Good luck!!!