The rules are unclear for *G. There isn't a rule saying your family members are exempt, but the website does say "Companions of elite members are also exempt from bag fees".
I'd definitely use the elite checkin and try to use that. If the agent hasn't done this before, they might give you the benefit of the doubt.
Skis count as a regular bag on UA. Although the rules say 1 pair of skis / bag, there were signs in SLC saying max 2 pairs / bag.
If you have to pay for extra luggage, it might be cheaper to pay for the skis. Internationally, they cost paid 1/3 of a regular bag fee.
Enjoy your ski trip
^