You didnt state how many are in the family; are you looking for a twin because of the people capacity, or because of safety?
Part 23 light twins are not required to climb on one engine, let alone maintain altitude. Some have higher service ceilings than others. I'd be a lot more concerned with performance than the difference in hourly fuel burn. Safety. It's your family, after all.
If you look at the mission cost for a dew annual trips set against the aggregate cost of ownership (maintenance, hangar, insurance, operation, training, etc), your hourly cost will be high; higher than renting, and more than likely much more than buying airline tickets. Especially after you factor in the acquisition costs.
Of the rwins you mentioned, the Seneca II/III has the better single engine service ceiling, but I'd look closely at 310's or a Barron. The 310 would be more economical, depending on model, and offer better overall and single engine performance.
Have a large cash reserve set aside for that first annual inspection; four or five times more than you think, no matter how good your pre-buy inspection. Be prepared to be surprised.