I have a Bard character I had a question about. Can I hold both a Rapier in one hand and a Whip in the other? So one round I can whip an enemy with a weak reflex save for example, and the next round if I wanted I could attack with the rapier?
Or I could use my rapier first and in the same round use Athletics Assurance to trip with my whip? Would that be allowed?
Yes. The whip is a normal weapon with which you can do any weapon stuff.
You could also for example trip with the whip from 10ft away and if successful step adjacent and the attack with the rapier with your 3 actions. If you are a fighter, you could also use Double Slice with Whip and Rapier first and then trip with the whip (with or without Assurance, however you like).
You can use your three actions in any way that you can imagine. Some actions actually cost two of those three actions, but it's usually pretty clear why.
In a single round you could attack with your rapier, then attack again with your rapier at -5, then do an assurance/Athletics check to trip with your whip.