2 sources 1 output

In my car I have two 12" subwoofers, and four 3 way speakers. The subs are powered by a separate amp from the other speakers all ran to a aux imput because my head unit was replaced incorrectly before I bought the car and I haven't been able to figure out why it will not work. But now my question. So my girlfriend wants to add a sub to her 2018 hyundai elantra. I will not change the radio in that just because I don't want to deal with it. But she still wants to be able to use the stock radio for the apple car play GPS and hear the directions and stream music at the same time. Could I run the door speakers to an amp with the sub for music and still keep the stock radio connected to only the door speakers for the built in navigation and Apple car play?

If you buy a dsp yes, but it’s easier/cheaper to change the radio