What is the ruling regarding girls and women who wish to wear the niqab, but their guardian refuses and subjects them to beatings and ill-treatment, forcing them to go out without it?

There is no sin upon a woman who uncovers her face due to compulsion. However, it should be noted that this applies when she is compelled or needs to leave the house. If this is not the case, then she must remain in her home so that she is not compelled to uncover her face.