My husband was previously married & had 2 children. His ex-wife has no legal rights, she did not sign her rights over, but she has no custody rights. His children live with his sister. My husband & his sister have joint custody. I was wondering what my legal rights are regarding the children. Would I be able to apply for joint custody (to have the same rights as my husband) or would I have to legally adopt them?

A step-parent has no legal rights regarding the step-children. So, yes, you would have to adopt them; which might require their mother's consent.

I was wondering what my legal rights are regarding the children.

Your legal rights are ZERO per cent.
Have a nice day and enjoy yourself!