Many thanks for your patience. I am pleased to be able to continue helping with your query now. First of all, I am sorry to hear about the situation you have found yourself in.
Your rights will very much depend on any contract that is in place, or in the absence of one, on any agreement you had with them over the hours or days or any other working arrangements.
In the absence of any actual agreement over this, whether written or verbal, they can potentially change your working pattern as they see fit and as the business needs dictate.
Having a child and being limited in your flexibility as a result, will not really give you any extra rights, particularly as you are self-employed. Had you been an employee, you would have had the right to at least make a formal flexible working request to try and agree on a pattern that suits you, but you do not get these rights as a self employed worker, unfortunately.
The self employed are often left in a difficult position where they have to juggle their work as best as they can, or not be able to do it, in the event the employer cannot be flexible with their requests. As you do not have legal protection over being asked to work hours which do not agree with your child caring arrangements, it means that you are left to try and resolve this directly with the company.