There's no particular reason why Pac wasn't on Doggystyle. Maybe Snoop just wanted to make an album without the biggest rapper so he could sell millions on his own, without riding on anyone's coattails. So he didn't dig up Wanted Dead or Alive, Out the Moon, Life So Hard (he did the chorus on the Gang Related version), Street Life, Bitches, or Just Watchin. The reason why Pac was on the albums of Daz, Nate, and Lady of Rage was probably to help them sell since they weren't really popular solo artists yet.
I don't think Pac and Snoop's "falling out" had anything to do with it, if it's true (debatable), it would've only been a small beef that lasted for what, Pac's last week or two of life? Most of which was spent in a hospital bed unconscious? It's not like they were best friends or anything, they were just cool with each other and two of the biggest stars on the same label. That's why Pac kicked it a lot more with the Outlawz, they were his lil homies. Just look at All Eyez on Me... two discs, and Snoop is only rapping on ONE song and adlibing on another. So don't be all surprised when Snoop has an album without Pac, he's always been an established artist, and Doggfather was already a highly anticipated follow-up to the biggest rap debut album at the time (until Eminem).