Steady on! In a turn the outer wing is going faster than the inner, but in a turn of 2nm radius at 250kt, for example, the percentage difference in forward speeds is tiny. In practice the effect only shows up in very small radius turns at low speed, so it is not a big aircraft problem.
If the outer wing is going faster it is again, technically, producing more drag, but not induced drag. Induced drag is a function of Cl, effectively of angle of attack, and is only directly related to speed when you look at the drag in straight and level flight, for in level flight angle of attack is related to speed squared.
Aileron drag only ocurs when aileron is applied, and while you may be holding small amounts of aileron on in the turn this is insignificant compared to the big drag input as you apply a lot of aileron to roll in or roll out. In fact, if our theory is right, and the aircraft is trying to roll into the turn because of the faster outer wing then you would be holding out-of-turn aileron which would give yaw into the turn, not out of the turn as does aileron drag as you try to roll in.
Don't get too tied up in this. Most of these effects are tiny (outer wing going faster) or are corrected by various fixes (adverse aileron yaw) The only critical one is - do not pull to the stall in a descending turn on finals.
Dick W