Is this close enough to what you need?
y4 = (A1 (-Fc-fl+A1 pL)(-((A1 beta)/(A1 sp+V01))-(A2 beta ?)/(-A2 sp+V02)))/mp^2+1/mp A1 wp;
y2 = (-Fc - fl + A1 pL)/mp;
result = Simplify[y4, y2 == yy4];
Simplify[result == (A1 yy4 (-((A1 beta)/(A1 sp+V01))-(A2 beta ?)/(-A2 sp+V02)))/mp+1/mp A1 wp]
returns True