Changing Job while on TN and getting TD visas

I changed jobs this week. Last Friday was my last working day with previous employer and I am going to the border tomorrow to get my TN Visa. There is going to be one week gap between two jobs

Does this imply, that my family does not need to get their new TDs visas as long as I maintain my TN status?

My wife TD was stamped from consulate in Toronto, Canada as she does not have Canadian passport yet. It is a valid 3 year sticker visa.
Does she need to make another visa application for her TD at the consulate?

They should be fine. It would have been "better" to go get the TN this weekend, but not a biggie. Their status is fime, as long as you do get your TN on this re-entry. Otherwise they will all need to return to border with you. Your wife does not need new consular visa as long as it is not expired.