Postgresql inheritance based database design
Whether you are better off with single-table-inheritance or class-table-inheritance really depends on the particulars of your case.  The performance advantage can go either way.  The difficulties presented by having lots of NULLS in a table range from the trivial to the overwhelming.
It depends on what your data looks like, and what you intend to do.

Kudos for figuring out that the problem is basically due to a mismatch between object modeling and relational modeling.

PS if you use UserID as the primary key on both Parent and Babysitter, and also declare it as a foreign key, you'll get some benefits, at the cost of a little programming when you go to insert new users.  This technique is called shared-primary-key, and it's also presented over on SO.