As per my knowledge the family (means wife and kids) will be under the sponsorship of husband. once your RP is expired, their RP also will invalid.

for example the companies have their CR, Computer Card, Municipality approvals etc etc. All employees can enter and exit if these documents are valid. once these are expired no body can enter or exit.

The same thing your family is under ur sponsorship and under ur RP. once it is expired their RP will be automatically expired.

This is a small information from my side. Get good advises from experts.