If you are a four year AROTC cadet, I believe that your only mandatory summer training is Advanced Camp in the summer between your MS-3 and MS-4 year.
If you skipped M-1 or MS-2 ROTC, you will likely be required to attend Basic Camp.
Other AROTC summer training such as CULP, Airborne, Air Assault, CTLT, are supplementary and are filled by the Cadre as space allows, usually with priority to the highest ranking cadets.