Launchpad is probably your best bet here. What kind of drum machine are you using?
You could use Ableton Link to keep your session in time. Auxy, Launchpad, plus many other apps play very nicely with Link. Launchpad unfortunately still doesn’t have Ableton Link start/stop, so your session will carry the correct tempo but you’ll need to hit play at the right time (within a scene) otherwise your scene starts will be off (which could make for happy accidents).
If you host Launchpad in AUM or perhaps AudioBus you can route midi apps to your drum machine. You can also use an app like Sync control (KORG) to sync link to pulse out (if it’s like a volca, or has similar timing inputs).
If you’re looking to mix tracks together you’re definitely going to want some kind of DJ app, Traktor comes to mind. There’s others. I’m not familiar with them really I’m not big on this kind of stuff. Launchpad does re-key and re-tempo loops nicely now, so you’ll have that functionality there, but as far as full length songs you’ll need something like Traktor.
Hope this helps some. There’s probably people on the Audiobus forum doing this kind of stuff already who could help you out there too.