Is it forbidden to dismiss a domestic worker, and what is the solution if her capacity for work becomes burdensome to the homeowner?

Your dismissal of this worker is not haram (definition), and it is not considered cutting off her livelihood, because her provision is from Allah, not from you. No one can cut off a provision that Allah has decreed for His servant, as He says: "Indeed, Allah is the All-Provider, Owner of Power, the Ever-Mighty," and He says: "Say, 'Who provides for you from the heavens and the earth?' Say, 'Allah,'" and the Prophet, peace and blessings be upon him, said: "Indeed, the Holy Spirit inspired in my heart that no soul will die until it completes its term and receives its full provision." However, it is not permissible for you to curse or insult her. Either you keep her, or you terminate the contract due to her not performing the work.