Estimating average daily consumption with samples randomly scattered in time
If you only want the average daily consumption over the whole period of time, you can simply calculate the difference between the last and first reading and divide by the total number of days.
As far as I understand your explanation:

your method 1 would not give you the true average over the period, unless you multiply each individual average by a weight corresponding to the number of days in the period.
your method 2 gives the true average, since it would represent every day individually (if I understand correctly)

However if you want to be able to observe the variations across time while smoothing some of the irregularities, you could:

calculate the daily average for every day like in method 2.
calculate a rolling average over a fixed number of days for every day. This is not perfect if there are long periods with no reading, but it should show the general trend better.
Plot a graph based on rolling average.