Can I change it to make my wife the family organizer?

Adding to the above, if there are children under 13 years old, the new organizer needs to leave the existing family, set up the new family, and then the under 13 years old children can be transferred to the new family. Then disband the old family and join the new family.

Family Sharing -  Transfer a child to a different family group - Apple Support     

You would need to disband the Family Group, and have her create a new Family Group, and invite the members to it.

See here: Leave Family Sharing - Apple Support