The way I'm reading this, the bride-to-be asked her sister to come to her house the morning of the wedding *and* planned ahead by requesting that their father pick up the OP and do the driving, leaving the OP's DH to follow later in their car with the children. I get the feeling the OP doesn't approve of having her father do the driving, but that's not the point.
Seems to me that the bride did take into consideration the distance and the fact the OP's family has only one car. I don't think we should consider her inconsiderate for that.
Whether the OP wants to give up a large part of the day to getting her hair done and watching the other bridal party members get their hair done is another issue, as is the cost. The BFing baby is probably the biggest issue, and is, to me, a reasonable excuse for not spending the morning at the bride's house.
But I don't think we should consider the bride rude or inconsiderate or unfeeling for wanting her big sister around while she's getting ready for her wedding day, or for making plans to have their father drive said big sister to her house.
(And if it were my father, he'd have been happy to escape the madness for a couple of hours, and delighted to have an hour to talk to his daughter all alone in the car without distractions. But fathers, as with everything else, may vary.)