FLUX, Did you use any flux on the copper when you soldered?
That's the only way the solder will flow and cover the pipe and fittings.
If you are only using the valve for the shower head, then yes, you could drill it bigger.
The reason it's a small hole, is to make sure the water goes through the tub spout first.
When the tub spout diverter is pulled up, it then moves water up to the shower head.