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 (sallallaahu 'alayhi wa sallam) is His slave and Messenger.
We ask Allah to grant you complete healing, leaving behind no illness, and to assist you in raising your children, and to bestow upon you abundant reward for caring for the two children.
If you are in need of exercising specifically at a gym, and there is no religiously impermissible issue involved—such as unlawful mixing, or photographing those who are exercising there—and you have done all that you can to request a reduction in the volume of the music, and you use earphones to listen to the Qur’an during your training sessions, then we hope that there is no sin upon you by joining this gym. However, it is preferable for a woman to exercise in her own home, by acquiring exercise equipment and the like, if that is possible.
Allah knows best.