Well it all depends on the chord progression. I don't know the chord progression to sweet child of mine, but if I'm just told that the key is D minor, well soloing in D natural minor, d harmonic minor, d melodic minor, d pentatonic minor, d phrygian, all will probably work, or at least they will all imply a minor tonality. If I knew the chord progression i'd be able to better say what scales it implies. Instead of thinking of it as switching scales, just think of it as him no longer using the natural 7, minor 6, or major second. D harmonic minor and d pentatonic minor have a lot of notes in common, (only the natural 7 vs minor 7 actually clash) and switching between them doesn't imply a change of the key of the tune but rather a change of choice on the soloists part.
I think you guys should think less in terms of scales and more in terms of chords and tones. You never have to play in a certain scale for a solo, and if you are thinking: "I'm sticking in D minor for this solo" it may hurt you and limit you. Instead, know what tones will sound strongest (if you're playing over a dm7 chord, the 1, b3, 5, and b7 will sound most consonant) and what tones will sound most dissonant (tones not in the scale) and what tones will create tension but not as much dissonance as the non scale tones (non chord scale tones.) That way your solos are likely to be less mechanical and more about creating sounds and melodies with notes, rather than playing fingerings corresponding to a key.