How to manage a PhD while being the breadwinner?

"Adjunct" faculty positions are not secure, don't pay well, and usually cannot be "parleyed" into full time spots, as many adjunct instructors mistakenly believe. Step one is to discuss the situation with your mom, and see what she thinks. Step two is to look at possible alternative financing. Visit the financial aid office of the university you are considering, and find out what help is available. Consider attending your graduate school program part-time, which will mean that the degree will take longer, but you'll ultimately get it. You will be able to do your best work in graduate school "fresh out of college." The longer the time between when you finish college and when (if ever) you decide to return to graduate school, the more difficult it is to get "back in the swing" of studying. Investigate carefully, and take whatever steps you can to earn the doctorate and get yourself the professorship you have dreamed of. The sacrifices will be worth it.

Being an adjunct does not pay worth a darn. But it depends on your PhD.. In the humanities and the arts there are almost nothing but adjuncts any more at low pay. My daughter got her PhD in civil engineering and works in industry and teaches one class per semester as a visiting professor. She makes as much doing that one course as an adjunct teaching three courses in the humanities. or arts.

My point its that is depends on your area of study.

It is your mother's responsibility to support her family -- not yours. And it is your and your brother's responsibility to pay for college -- not hers.

You and your brother should STOP accepting money from your mother immediately. She should support herself, and you should each support yourselves.