I don't know, can you?
1. What is the voltage of the battery? What voltage does the Mini require?
2. How would you charge the laptop battery?
3. What issues are there that you may have to deal with when connecting a battery inline with a car power supply?
4. Why would you want to do this? What advantage do you gain vs. an alternative arrangement? Would you use a tank circuit or would you power the Mini from the battery itself?
Lay out the alternatives and you'll see some of the issues. Hint: search for information on tank circuits. There's even some information in the FAQ to the FAQs in the FAQ Emporium.