Block Diagram Simplification and Routh-Hurwitz
Lets start by labelling your first effort 

We will call the bottom block \$ G_3 = \frac{G_1}{1+ G_1 \cdot H_1} \$

The top block \$ G_4 = \frac{G_2}{1+ G_2 \cdot H_2} \$ 

For convenience I've dropped the (s) notation from \$ y \$ and \$ u  \$ since we know they are functions of s.

I've also added labels: 
\$ w \$ is the input to \$ G_4 \$,\$ x \$ is the output of \$ G_3 \$

Now lets simplify further

\$ y = x + w \cdot G_4 \$

\$ w = u - x \cdot H_1 \$

\$ x = u \cdot G_3 \$

We want \$ \frac{y}{u} \$

\$ y = u \cdot G_3 + w \cdot G_4 \$ 

\$ w = u - u \cdot G_3 \cdot H_1 \$

\$ y = u \cdot G_3 + (u - u \cdot G_3 \cdot H_1) \cdot G_4 \$

\$ y = u \cdot  \left( G_3 + G_4 - G_3 \cdot  G_4 \cdot H_1 \right) \$

If we now replace \$ G_3 \$ and \$ G_4 \$ with their definitions and these by their transfer functions (in \$ s \$) we have the transfer function for the entire system. Can you take it from here?