How should I wire two batteries to make my mobile DVD player work longer?
Series batteries is not what you want to do. If you connect them in series you will double your voltage and the DVD player probably wont be able to handle double the voltage. What you need to do to increase your life in this case is to put the batteries in parallel. This question explains a bit more about series/parallel.

The problem with this is that the batteries will drain at different rates, especially since they are rated for different mAh. When this happens you will end up having 1 battery charging the other battery, which is not exactly ideal.

To answer your specific question about what the 3rd wire is for, most likely this wire is a center tap between the 2 cells in the battery. This is used to be able to charge each cell independently of each other. If you don't have this connected, or connect the two batteries together, you will most likely cause the charging circuity in the DVD player to do some bad things.

My overall recommendation would be to just buy a single new batter with a greater mAh.