Your sentence is interesting, because as you suppose, “de” can have both the English meanings you gave as an example, though your example “1” would rather be used with “reçu“:

“J’ai reçu de l’argent de mon frère“: Here, “de mon frère” is not a complément de nom to “argent“: in fact, this bold “de” goes with “reçu” and not with “argent”: It would be as correct to write this sentence like this: “J’ai reçu de mon frère de l’argent“, or to replace “de” by “par”: “J’ai reçu de l’argent par mon frère“.

In your example “2”, “J’ai de l’argent de mon frère”, the bold “de” links “argent” to “mon frère” as a complément de nom.

To summarize, the difficulty you show comes from the fact that the preposition “de” can have two different meanings: “de mon frère” car either mean “from my brother” or “of my brother“, as you rightly supposed, but in your example 1, a French speaker would not say your sentence without adding “reçu”, as quoted above.