preocuparse por = to worry about (angustiarse/inquietarse)
preocuparse de = to be concerned about; to care about (ocuparse de)
There are those that use por or de when the meaning is 'to worry about' (angustiarse).
In either case, the preposition is always used when the verb is followed by an infinitive (what you're calling a second verb).
An infinitive acts as a noun. (In this role, it is a prepositional object.)
Me preocupo por mi hermano. = I'm worried about my brother (I'm distressed).
Me preocupo por aprobar el examen. = I'm worried about passing the test (stressed because I didn't study enough).
Me preocupo de aprobar el examen. = I'm concerned about passing the test (concerned, so I'm studying hard).
And, in your example about your mother worrying about buying more clothes, it is because she doesn't have the money to do so (she's distressed).
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