You’re right though, it’s probably time to move on, it’s just the lack of reply, if he were to say no, that would be fine, at least i’d know
Take his lack of reply as no and look for new clients.
As @Digdongdoo has said, you're the professional, not the family you're working for. As a professional, it's up to you to have proper terms and conditions in place, that the family is aware of from the very beginning, so that clients don't think that they can treat you however suits them. Your failure to set out terms and conditions initially with this family led to them treating you in the way you've described above.
If you're planning to contact new people after the weekend, then spend the next few days drawing up your terms and conditions to present to new clients. So that everyone is clear how the relationship will work from the beginning.
Ensure you ask for payment in advance to avoid being left out of pocket. Make it clear what date you expect payment by. E.g., if you want clients to pay a month in advance then ask for payment by the end of, say March for example, to cover April's tutoring sessions. Or perhaps you want clients to pay by term. As it's your business you can set the rules. If they want to quit tutoring how much notice is required? What is the cancellation policy if they need to cancel a session? What happens if you need to cancel? What hours are you both agreeing to, rate of pay, etc. Agree what will happen over short holidays such as Easter, Christmas and what the options are for summer holidays. Lots for you to think about. All of this information should be presented to potential clients.
Make sure you work out what you need to earn so that you can save for quiet times, such as summer holidays.
Despite what you may think, lots of posters are trying to help you, so ask if you need help drawing up terms and conditions. Or give an example of your draft contract and posters can point out any weaknesses so that you can avoid being in this uncertain position again.