Analyzing circuit with two transformers in parallel
There are a few models that you can use:

The transformer equations for an ideal transformer with resistance are as follows:

$$ V_1 = L_1\frac{di_1}{dt}+M_s*I_1$$
$$ V_2 = L_2\frac{di_2}{dt}+M_s*I_2$$

Ms is the coupling coefficent.





There is the T-model which might be useful in simplifying inductors




Matrix math might be good at this point (write out a series of equations)
Good luck on the simplification