mstram
If you want to see why the AOA increases on the leading wing during a sideslip then take a sheet of A4 paper and fold it in half (short side to short side) crease the fold and then open the sheet to represent a wing with a modest dihedral angle. Hold the paper up in front of your face looking along the crease line as if the dihedral wing is flying towards you. Tip the crease line slightly leading edge up so that you see the underside of the wing. Note you see the same amount of the bottom of both surfaces. Now apply a slip angle and notice how you (the oncoming airflow) now sees the bottom of the leading wing but the top of the trailing wing. This asymmetry in AOA has come from the geometry of the dihedral angle.
As has been said there is a bit of work needed to feel at home in the air and be quite confident that you know what you are letting yourself in for when it comes to using slipping turns on finals..
The following may help (sorry if it is a bit basic)
1 At a safe height start with a straight descent in the landing configuration at your typical approach speed. Trim it and let go of the wheel or stick.
2 Smoothly apply some rudder. If the aircraft changes its bank angle then the aircraft has dihedral effect (whether or not the wing has dihedral angle).
3 If the roll is in the direction of the applied rudder then the dihedral effect is said to be positive (which is normal on certificated aeroplanes) and the roll arises from an imbalance of lift resulting from an increase in the AOA of the leading wing and a decrease in the AOA of the trailing wing. (as you saw with the paper)
4 Counter the roll with aileron and adjust the bank until your heading stops changing. You are then said to be doing a ‘steady heading sideslip’ beloved of certification and flight test communities as a means of gaining data about a variety of subjects. You will now need a lower nose position to maintain your original IAS due to the drag of going sideways. Thus a sideslip is useful as a means of increasing your descent rate without increasing speed as well as improving your view in the direction you are travelling (not the direction you are pointing).
5 The significance of doing all this in a turn (sticking on rudder and countering the roll with aileron) as opposed to straight flight is that for a given airspeed the AOA values of both wings will be higher because you are turning. This means you are closer to the stalling AOA than in steady heading flight. Just as you are in a balanced turn when compared to balanced straight flight if both are at the same IAS.
6 If you fly slow enough or turn tight enough or a combination of both you will stall any aeroplane. Doing this at a time you have rudder applied turns this stall approach into a spin entry manoeuvre.