Control Systems - State equations
It seems like the issue you're having trouble with is how to incorporate transfer function zeroes into a state space model.  Once you can do that, the rest of your question might become easier.

I think the presentation in Dorf and Bishop on this matter is pretty clever.  Let's take your second-order subsystem $ G(s) = \frac{Y(s)}{U(s)} = \frac{s+4}{3s^2+5s+6}$ as our working example.

Inject a factor of unity into this expression and you get

$$\frac{Y(s)}{U(s)} = \frac{s+4}{3s^2+5s+6} \frac{Z(s)}{Z(s)}.$$

If all the fractions are fully reduced, we can match the numerators 
$$ Y(s) = (s+4)Z(s) $$
and match denominators
$$ U(s) = (3s^2+5s+6)Z(s).$$

The inverse Laplace transforms of these equations suggest the following time-domain differential equation relationships

$$y(t) = z^\prime(t) +4z(t)$$
and 
$$u(t) = 3z^{\prime\prime}(t) +5z^\prime(t) +6z(t).$$

We have at most two derivatives of this weird $z(t)$ function, so let's climb the ladder when defining our state in terms of $z(t)$:
$$x_1 = z \\ x_2 = z^\prime.$$

Can you deduce the A, B, C, and D matrices from here?