On works with both meanings here:

• On can indeed be the impersonal pronoun here. "On s’en fout" should be understood as "nobody cares".
• "On" can also be understood as "we" in this context, as "you and I": the mother says "we don’t care about the purse", which actually expresses the idea "you and I should not be talking about the purse, I want an explanation about something else (ie the condoms)".

S’en foutre is not a fixed expression. Yet, it is often used as the short form with the pronoun "en", especially as spontaneous reaction (je m’en fous !). But, if you feel that it wasn’t clear enough and you want to specify what the "en" refers to, or put the emphasis on it, you can add the complement (grammatically, it is then rather a repetition of the complement, and strictly speaking, should be preceded by a comma in the written form):

Je m’en fous !

Je me fous de ta nouvelle voiture.

Je m’en fous, de ta nouvelle voiture !

Je me fous de ce que tu penses.

Je m’en fous, de ce que tu penses !

This construction is pleonastic in reason of the use of “en”; LBU 14th ed., states this fact p.876 § 680 c) 4° and gives the following examples.

• J’EN AI bien ASSEZ DE la campagne, et je n’y remets plus les
  pieds !… (BALZAC, Pet misères de la vie conjug., PL, p. 241.)
• J’EN AI ASSEZ DE ces cocos-là. (FLAUB., Éduc., III, 3)
• J’EN AI ASSEZ DE ces bavardages ! (Ac. depuis
  1980.)

• J’ai dit que J’EN AVAIS MARRE des embusqués de l’arrière (DORGELÈS,
  Croix de bois, XV).

  It is a usage that belongs to the spoken language, as I see it;

The use of “on” is ambiguous here; it is normally used to replace “nous”; if this were so, it would mean that either the mother and the daughter do not care about the particular attitude of the mother regarding her daughter’s belongins, which is not quite intelligible since the daughter does care or that “nous” means some other group in which the daughter is not included, and that is not a definite group, it remains undefined. In either case we are dealing with incertitude. A third possibility, that is that which consists in using “on” as a replacement for “je” is extremely unusual. In the end one does not really know, except for the fact that the mother is in the group. Another interpretation for the ambiguous usage of “on” is that the speaker intimates the person he/she is talking with to abandon their concern as he/she do not share it, imparting strongly to them the idea that he/she is not going to take this concern into account; that is also not said in a definite manner but remains a likely possibility. Because of the vagueness of this type of enonciation, I think it should be avoided.