I don't think that Dolphin could cause your Wiimote to use up power more quickly. The only thing I can think of is that the Wii will automatically shut off your Wiimote if you are idle, while Dolphin will not, so you have to make sure to manually shut off your Wiimote after you are done playing. Also, the Wiimote will use more energy when pairing, since it cannot remain permanently connected to your computer as it does with a Wii, but I don't think that this extra power usage is noticeable.
Perhaps your batteries are getting older? Rechargable batteries lose efficiency with age. It could also be, as you said, an inaccurate reading (not Dolphin's fault, but sometimes the Wiimote gets it wrong). Keep playing and see how much longer the batteries actually last.
Perhaps your batteries are getting older? Rechargable batteries lose efficiency with age. It could also be, as you said, an inaccurate reading (not Dolphin's fault, but sometimes the Wiimote gets it wrong). Keep playing and see how much longer the batteries actually last.