Hello, fellow non-trad here
I think you should seriously consider what Peaches is saying: 1) your connections in no way guarantees you a job anywhere and 2) you need FULL-TIME legal experience before graduating. So although I think it's fine that you'll be taking summer classes this year, you should definitely try to get full-time experience next summer. Basically, I just don't believe that the benefits of graduating a few months early outweighs the costs of foregoing substantive full-time legal experience.
You may not think that there's much of a difference between working full-time vs. part-time at a legal internship, but there is. The difference is much more visible when you have both full-time interns and part-time externs working at the same time. It is easy to overlook the part-timers when you have a full-timer constantly there. The full-timer is likely to get the choice assignments first because: 1) the full-timer simply happened to be there when the project came up and the part-timer was not present 2) the full-timer has more time to express a preference for certain kinds of work 3) there is a short turnaround time required of an assignment and the part-timer would not be able to complete the assignment in the time available. The part-timer may thus get relegated to non-legal work, like clerical tasks or paralegal tasks. Another factor is that you simply get more face time with the attorneys as a full-timer and are more likely to be invited out to social events. As the BigLaw model of summer associates show, sometime internships are less about the substantive experience and more about the networking
Unfortunately, sometimes non-trads have a harder time finding a job right out of law school. Part of this is due to age discrimination. Part of this is due to the fact that non-trads often over-estimate the extent to which their past experience and prior connections will help them with starting their new career as an attorney. True, a prior successful career can help you stand out in a field of applicants, but legal employers are more concerned with substantive legal experience. This is why someone who went to law school straight from undergrad but had two full-time legal internships may be more likely to be hired than someone with 10+ years experience in a related field (i.e. a former engineer/project manager wanting to go into IP law) but chose not to get full-time legal experience.
Lastly, I think it would behoove you to get legal experience from someone other than your brother. At most interviews, you will be asked how you got the previous job. Working for family may not be taken as seriously, especially if it was only part-time.