How do you translate a per year salary into a part-time per hour job?
If you're really a part-time worker, then there are some simple considerations.... The remote working environment, choice of own hours, and non-guarantee of work availability point to your "part-time" situation being more like a consultancy, and that would normally double or triple the gross hourly rate. But if they're already offering or paying you a low hourly figure, they are unlikely to give you consultant rates.