Yes, it's appropriate as a neighbor who is dealing with a crying dog. You need to discuss this with them face to face or come up with another plan. They are entitled to not be disturbed by your dog, just like you are entitled to not have them turn up their music at odd hours of the night.
I've never seen anything in any Landlord Tenant act that prevents a landlord from calling or texting a tenant. If they access your space, you are generally entitled to 24 hours notice except for emergencies.
Look up the NY landlord tenant act to be certain of your rights and responsibilities, but they are also entitled to live in peace too.