To be more precise, if you have appropriate DNA matches to your mother, your brother, and your nephews, that confirms the biological relationship that you undoubtedly always believed you had. If you DON'T happen to match your mother, that would indicate that you're adopted, or something like that. If your match to your brother isn't what it should be, it might mean that you had different biological fathers.
But chances are, they're all turning out to be biologically related exactly the way they're supposed to be. That doesn't mean that it didn't tell you anything - it's just that it's confirming what you already thought you knew.
For the purpose of pursuing the kind of investigation you're talking about, however, if you have access to your mother's DNA then you should only use that one. Everybody else (you, your brother, and his kids) can only have SOME of the DNA she has, so they are all less useful than her test, and none of them tell you anything that hers doesn't.
The answer lies in who you mother matches. Is there somebody within her matches who is a descendant of that suspected "second family"? That's the question. If not, you might try asking them whether they have tested (with the same company). Anybody who is at least a half-second cousin to your mom will almost definitely show up as a DNA match to her. If they haven't tested, see if they'll test (offering to pay for it yourself might help sometimes).