I would definitely go for "To my wife, children, parents and mentors". You honour them by naming every one of them, I wouldn't worry about wordiness. One consideration to take into account is:
Think not just about the person or people named in the book dedication, but also about all of the readers who will pass by this page and be impacted. Make a conscious choice about what you want that impact to be (if any). (Medium.com)
As for the technical term, some use immediate family, which
normally includes a person's parents, siblings, spouses, children, or an individual related by blood whose close association is an equivalent of a family relationship. (Wikipedia)
In law they also use the phrase close family member which includes:
the individual's spouse; the individual's and the spouse's
grandparents, parents, siblings, children, nieces, nephews, aunts,
uncles and first cousins; the spouse of any of these people; and any
other individuals who share the same household with the Government
Official. (Lawinsider) - includes too many.
There doesn't seem to exist a name which would include only your wife and children (and parents).