In Bustin' Out mode, the people who you live with cannot get fired. If you want them to stay home, just let them. This can be very useful if you need them to clean up, or need them to do some other things.

While living with Mom, do not run out and get a job after you have completed the first few goals. Instead, stay around awhile and use that time to build skills. Mom will nag you, but just select 'Okay' and keep doing everything else. Make sure to keep yourself happy and entertain/talk/joke with Mom to keep your relationship up to par. When you have your skills where you want them, move out. This will make things much easier. You will then be able to concentrate on your job and relationships, rather than skill building.