Let me get this straight they wish you to now
turn over guardianship not just express your wish for them to be backup guardians if something should happen to you?
That does not smell right in any way or in any manner should that be the case.
In any regards, paperwork or no paperwork a court would likely need to review the issue of guardianship however your express wishes would carry great weight and even more so if your husband would sign on.
Still there is something wrong as your husband even in jail after your death could grant guardianship to your parents in case of need if you both would be on the same page over this matter.