When you tighten that p-trap, start to tighten the other two slip joint nuts but leave them a bit loose.
Do the final tighten on the swivel nut first.
You are right, this one needs to be centered, and if the other nuts are tightened first, you won't be able to center it.
So...tighten the swivel nut, and then the other two.
And you should be fine.