How to say "mix of two language" in a bad meaning
The two categories are creoles and pidgins. They're both "mixed heritage" languages, but only creoles have native speakers (so only they can really be said to have functional grammar).
Arguably therefore, pidgin is more derogatory, since it usually applies to less-developed languages. On the other hand, you might think "parvenu" creole children would be looked down on by native speakers of the contributory languages (as lacking any clear linguistic/cultural heritage).
There's also barbarous language, barbaric language, and barbarisms (which are often linguistic). And for those who don't know the etymology of barbarian...
To the Greek ear, someone who did not speak the Greek language babbled, producing the onomatopoeic sound “bar bar bar” which became bárbaros, and later barbaria in Latin.
How about "pidgin"?
From wiki: "Fundamentally, a pidgin is a simplified means of linguistic communication,.. Pidgins usually have low prestige with respect to other languages."