What is up with us "don't want to be rude?" folks? I think the bigger problem is, you thinking about this way too much.
You don't need to be witty about this. Only polite, yet frank.
"I am sorry Renae, I don't think I will be able to pick you up. If you cannot get here without me, that means we will not be able to see each other this time around. That makes me sad but it's OK, we'll have to try to meet up again next time."
If Renae asks for an explanation, tell her the truth, but don't overexplain or try to make excuses...
"Well, it will be a six hour drive to and from to get to you. I have my daughters to think about, I will not leave them home unattended if my husband is working and I cannot get a babysitter on time on a school night. I cannot also guarantee that I will be available since my husband's work obligations might mean we have to travel with him. I wish we could meet up Renae, but I just cannot commit to it right now."
If she is a true friend she will understand completely.