One dog per person under the seat, so unless it's Jere, her DH and one other person, that only takes care of two of the Dachsies. The larger dog could fly in cargo if there is space available. It's a pressurized cargo hold and there's only room for one or two dogs per flight. So yes, the dogs can fly with you, but four is a bit much to deal with.
Elizabeth (who has flown with dog as far as Poland and back)