Is the following formula in DNF?
$$((P \land Q) \land ( \neg R \land \neg S)) \lor ((r \lor s) \land (\neg p \lor \neg q))$$
I think it is not a DNF, because in the second part there are OR's inside an AND. Is this correct?
How should I rewrite this to a proper DNF?
You must simply expand it performing the AND's in the second part (following the same rule as if AND were a multiplication and OR an addition), so obtaining: $$(p\land q\land \neg r\land\neg s)\lor(\neg p\land s)\lor(\neg p\land r)\lor(\neg q\land s)\lor(\neg q\land r)$$