All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The basic principle is that taking care of your husband's child from another woman is not obligatory for you. If you had promised to volunteer to do so and then realized that you are unable to look after the child, there is no blame in retracting this promise. Apologize to your husband and explain to him that you are unable to take care of his child.
Allah knows best.