Is it permissible to perform only the five prescribed daily prayers without the Sunan and without accompanying one's mother, and is it permissible to refuse to go with one's mother to the market when one is tired?

There is no sin in abandoning the supererogatory (Sunnah) regular prayers, but one should not neglect them. There is no sin upon you if you attend to your mother and do not pray the Sunnah prayers, but it is preferable to combine both matters if your mother is not harmed. It is obligatory to obey your mother regarding going to the market to help, unless there is real harm to you, or if the market is a place where one cannot avoid evil.