With Rakish Audacity, an initiative roll is d20+Dex+Cha
An initiative roll is, by definition a Dexterity check:
When combat starts, every participant makes a Dexterity check to determine their place in the initiative order.
Thus, an initiative roll will, by default always involve adding your Dexterity modifier (unless a feature tells you otherwise).
Rakish Audacity defines itself not as a replacement to that Dexterity modifier, but as a bonus to that roll:
You can give yourself a bonus to your initiative rolls equal to your Charisma modifier.
Since Rakish Audacity says that is is a bonus to that roll, it gets added on top of that normal Dexterity check.
So, for your specific example, the initiative check would be: $$10(d20) + 3(DEX) +2(CHA) = 15 $$
Jeremy Crawford has clarified via Twitter and agrees with this interpretation:
Initiative is a Dexterity check. Rakish Audacity lets you add your Cha. mod. to that check; it doesn't replace the Dex. check.