The mother is the result of live bacteria eating the sugar from the apple juice and why it creates a thick rubbery mass that floats on top, I do not know. I do know if you bother the mother, it will sink to the bottom and then make a mess of the vinegar.
The 5 gallon water jug is good in the short time, but does not allow enough air in general, your best with 5 gallon bucket and a tight cloth such as a bath towel stretch accross it, this allows enough air and keeps bugs out.