The subs function can be used to "plug in" values for the C'(t) equation.
In this answer, I use the Symbolic Math toolbox syntax from MATLAB R2016b. If you are using a previous version of MATLAB, you may have to adjust the syntax before using this code.
To elaborate further on your example, if A, B, and C are defined as symbolic functions of t:
and eqA, eqB, eqC, and eqDC are the defined symbolic equations:
eqA = diff(A) == 2*A
eqB = diff(B) == 3*B
eqC = C == A + (B*B)
eqDC = diff(eqC)
then the subs function can be used as follows to substitute eqA for dA/dt:
eqDC_subA = subs(eqDC, diff(A), eqA)
and can be used for eqB too:
eqDC_subA_subB = subs(eqDC_subA, diff(B), eqB)
Please refer to the Symbolic Math Toolbox documentation for the subs function for more information: