You urgently need to reconfigure your MoPi. The battery datasheet gves an absolute minimum cutoff voltage of 10.5V. Going down to 9.48V will kill your battery fairly quickly. The maximum voltage will be something like 12.8V under load when fully charged - check this with a DMM and use the actual value. As a rule of thumb, without a smart charger you can only safely use 50% of the nominal battery capacity, as it never gets fully charged if you only charge it to the maximum float voltage of 13.8V and you always want some margin on the low end to reduce the risk of premature failure. 30% is a good cut-off point for practical cyclic applications, but the actual voltage depends on the discharge rate.
You *WILL* need some sort of charge controller to avoid overcharging in the summer.
The Pi 2's idle current with no peripherals connected apart from Ethernet, is probably somewhere around 0.25A. WiFi dongles tend to be power-hungry. Hardwire the Ethernet!
If you are running this 24/7, that's 30WH/day. It wpuld be advisable to log the actual current drawn from and voltage of the battery over a 24H period running your actual applications so you can refine the power budget calculations. Your nominal 2W panel, best case will give you something like 15WH/day and worst case, in the month of June will average around 8WH/day. See http://aussiervproducts.com.au/solar-mapping
IMHO you'll need something like four or five times your current panel area to keep the battery charged under worst case conditions, as you must allow for losses in the charge controller, the battery itself, and in the MoPI.