There's no such thing as holding two different pilot certificate. You are issued one certificate, which you hold at the ATP level.
You can obtain various privileges on your certificate, given at whatever level you wish to attain.
If you currently hold an ATP pilot certificate with a rotorcraft category rating, and a helicopter class rating, then you've already got your pilot certificate. You can't obtain a private pilot certificate, and don't need one.
What you do need is a new category and class rating on your pilot certificate, and you can obtain that at the private pilot level. You'll need an airplane category and Single-Engine Land class rating.
In order to obtain the Airplane, Single-Engine, Land category and class addition to your pilot certificate, you'll need to pass the practical test at whatever level it is at which you intend to seek pilot privileges. You've expressed a desire to hold private pilot privileges in single engine airplanes, and therefore must pass the practical test in accordance with the practical test standards at the private pilot level, in a single engine land airplane.
You can find the test standards at
http://www.faa.gov/training_testing/testing/airmen/test_standards/pilot/media/FAA-S-8081-14A.pdf
You can see the various levels of pilot certification, as well as the applicable category and class ratings at 14 CFR 61.5, at
http://ecfr.gpoaccess.gov/cgi/t/tex...iv8&view=text&node=14:2.0.1.1.2.1.1.5&idno=14
You can read about the requirement to add a category and class rating to your pilot certificate by visiting 14 CFR 61.63 at
http://ecfr.gpoaccess.gov/cgi/t/tex...iv8&view=text&node=14:2.0.1.1.2.2.1.2&idno=14
§ 61.63 Additional aircraft ratings (other than for ratings at the airline transport pilot certification level).
(a) General. For an additional aircraft rating on a pilot certificate, other than for an airline transport pilot certificate, a person must meet the requirements of this section appropriate to the additional aircraft rating sought.
(b) Additional aircraft category rating. A person who applies to add a category rating to a pilot certificate:
(1) Must complete the training and have the applicable aeronautical experience.
(2) Must have a logbook or training record endorsement from an authorized instructor attesting that the person was found competent in the appropriate aeronautical knowledge areas and proficient in the appropriate areas of operation.
(3) Must pass the practical test.
(4) Need not take an additional knowledge test if the person holds an airplane, rotorcraft, powered-lift, or airship rating at that pilot certificate level.
(c) Additional aircraft class rating. A person who applies for an additional class rating on a pilot certificate:
(1) Must have a logbook or training record endorsement from an authorized instructor attesting that the person was found competent in the appropriate aeronautical knowledge areas and proficient in the appropriate areas of operation.
(2) Must pass the practical test.
(3) Need not meet the specified training time requirements prescribed by this part that apply to the pilot certificate for the aircraft class rating sought; unless, the person only holds a lighter-than-air category rating with a balloon class rating and is seeking an airship class rating, then that person must receive the specified training time requirements and possess the appropriate aeronautical experience.
(4) Need not take an additional knowledge test if the person holds an airplane, rotorcraft, powered-lift, or airship rating at that pilot certificate level.
You will not need to take an additional knowledge ("written") test. You also do not need to meet the specific training time requirements for adding a class rating, but in this case you're adding a category rating as well...and need to meet all the category addition requirements spelled out in the regulation.
You can read the certification requirements for private pilot privileges in a single engine land airplane by visiting 14 CFR 61.103, 61.107(b), and 61.109(a).
§ 61.107 Flight proficiency.
(a) General. A person who applies for a private pilot certificate must receive and log ground and flight training from an authorized instructor on the areas of operation of this section that apply to the aircraft category and class rating sought.
(b) Areas of operation. (1) For an airplane category rating with a single-engine class rating:
(i) Preflight preparation;
(ii) Preflight procedures;
(iii) Airport and seaplane base operations;
(iv) Takeoffs, landings, and go-arounds;
(v) Performance maneuvers;
(vi) Ground reference maneuvers;
(vii) Navigation;
(viii) Slow flight and stalls;
(ix) Basic instrument maneuvers;
(x) Emergency operations;
(xi) Night operations, except as provided in §61.110 of this part; and
(xii) Postflight procedures.
Note that while you've already demonstrated all of the above in a helicopter, you haven't demonstrated it in a fixed wing airplane for the purposes of certification...and will need to demonstrate these things as part of a practical test before either an FAA inspector, or designated examiner.
§ 61.109 Aeronautical experience.
(a) For an airplane single-engine rating. Except as provided in paragraph (k) of this section, a person who applies for a private pilot certificate with an airplane category and single-engine class rating must log at least 40 hours of flight time that includes at least 20 hours of flight training from an authorized instructor and 10 hours of solo flight training in the areas of operation listed in §61.107(b)(1) of this part, and the training must include at least—
(1) 3 hours of cross-country flight training in a single-engine airplane;
(2) Except as provided in §61.110 of this part, 3 hours of night flight training in a single-engine airplane that includes—
(i) One cross-country flight of over 100 nautical miles total distance; and
(ii) 10 takeoffs and 10 landings to a full stop (with each landing involving a flight in the traffic pattern) at an airport.
(3) 3 hours of flight training in a single-engine airplane on the control and maneuvering of an airplane solely by reference to instruments, including straight and level flight, constant airspeed climbs and descents, turns to a heading, recovery from unusual flight attitudes, radio communications, and the use of navigation systems/facilities and radar services appropriate to instrument flight;
(4) 3 hours of flight training with an authorized instructor in a single-engine airplane in preparation for the practical test, which must have been performed within the preceding 2 calendar months from the month of the test; and
(5) 10 hours of solo flight time in a single-engine airplane, consisting of at least—
(i) 5 hours of solo cross-country time;
(ii) One solo cross country flight of 150 nautical miles total distance, with full-stop landings at three points, and one segment of the flight consisting of a straight-line distance of more than 50 nautical miles between the takeoff and landing locations; and
(iii) Three takeoffs and three landings to a full stop (with each landing involving a flight in the traffic pattern) at an airport with an operating control tower.
This above quote is perhaps the most relevant to your question. While you hold ATP privileges in helicopters and have pilot experience at that level, and have demonstrated skill at that level, you're still required to undergo the requisite instruction in a single engine airplane (because you're adding a category rating to your certificate...
you wouldn't need to do all the training prescribed, if you were only adding a class rating...eg, if you already held an airplane category rating with another airplane class rating such as multi engine land). This includes dual cross country flights, night flights, etc...which must be done with an instructor in a single engine airplane.
