When you apply a Second Chance all your Heros Skill points are reset (removed from current skills) both for Main Hero Skills and for Invader Hero Skills. You can redistribute your skills as many times as you like but it cost one Second Chance to do it. There is currently no method to just move a part of your points or have any preset schema to set all points directly, you must reapply each point one by one.
Tips: Check your current points before you clear skills, it may help you to reapply better
Tips: Building speed I and Learning Speed I gives more speedup for less points than Building Speed II and Learning Speed II, but Stone Production III (350% and 50 skill points) gives more than Stone Production II (65% and 20points). It MAY give better return to skip lower skills. Please do the math.
See also list of Skills