1.5W from the solar panel won't be enough -- especially since that will be available on average less than half the time. The RPi boards seem to use around 0.7A at 5V (3.5W),. maybe more or less depending on peripherals, but not under the 0.5W average you might get from the 1.5W (peak?) panel. I'd be looking for a 5-10W panel to keep the system alive. The 50Ah battery is more reasonable, especially if that is 12V and you have an efficient switching regulator to 5V. It might struggle in cloudy weather in winter. (Where is this system? How much sunshine?)
VNC won't add to the consumption.
"If it ain't broke, fix it until it is."
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