When it comes to verbal negation, dummy DO occurs in negative imperative clauses and negative clauses with a primary verb-form (i.e., the preterit, 3rd person singular present, or plain present form) without another auxiliary verb present.
Since subjunctive clauses aren't imperative clauses, and they aren't headed by a primary verb-form (namely, they have a secondary verb-form—the plain form—as head), they don't qualify.
For more details, see A Student's Introduction to English Grammar by Huddleston & Pullum (2005).
As an aside, to make things completely clear: it's absolutely grammatical to use different mandative constructions, such as the one in the second sentence – a so-called covert mandative (where doesn't would be the normal choice in that particular case, sanctioned by the use of a primary verb-form without an auxiliary).
It should also be noted that these constructions occur with (appreciably) different frequencies in different dialects.
Reading the sentences again, the second one leaves some room for ambiguity as well, but I think that's out of scope for this question.