In my opinion it is definitely not a matter of letting time take care of the problems.
Suggestions:
Look into a puppy class, not training but socializing, your brother & Alexandra can go together with Sugar.
Look into doggie day care programs both dogs can go to while your brother is at work. A good doggie day care program will be clean, friendly, have nice dogs, and people who will work on socializing Sugar.
If neither of the above are options, ask the vet to suggest an animal behaviorist who can do a few private sessions at the house, access the situation & teach your brother & Alexandra the best way to motivate Sugar to be more confident.
Remember it is very important for a puppy to be well socialized to the outside world of people, dogs, sights & sounds. Sherlock was very shy with people so we took him into town almost every day. If you like I can email our methods in more detail.
When it should be time for Sugar to use the pad, I suggest taking her outside along with her pad. Put the pad on the grass and see what happens. A book to read while they wait might help.