My mother wants to take custody of my daughter for I got married to someone who is now in prison and thinks she is at risk. Can she legally do that?

If you and the dad agree to it then you should be able to.
You can also check into giving her guardianship or temporary custody.

Can you define what she's at risk of ? It can't be your husband if he's in prison. Is she claiming you're the danger to the child and why ?

Most likely no she can not take custody away if you are not a danger to your child. She will have to prove that the child is in danger and you are not a fit mother to get custody away from you.