I don't think there is a way for the OP to get everyone upgraded without one supporting at least one family member with instruments.
UA's UDU program extends the complimentary upgrade to one other person on the same PNR as the elite member (in other words, two people).
Related thread:
http://www.flyertalk.com/forum/unite...-question.html
As suggested above, the optimal strategy for UDU would be each 1P member to have their own PNR with one family member. Under UDU, up until the upgrade list goes to Departure Management, the upgrades will clear based on the 1P member's status. When it goes to DM, the queue is resorted to each member's status.
That still leaves out one GM family member.
Depending on the route and equipment, the chances of a flight being >NF5 (which would allow the entire family to have upgrade seats available to them) for a 1P might not be very likely.
The last time I checked, UA's rules for E+ for 1P members is similar to UDU; only one additional guest can be seated in the E+ area (doesn't need to be on the same PNR, though). So, if you want E+ seating, a fee is going to apply for one family member.