Equilibrium, Kp constant, Partial Pressures
The method referred to in the comment is not correct and is a common mistake. One may think,

$$p_1'+p_2'=p_t\frac{V_t}{V_t'}=2p_t=0.88 \rm atm,$$

but this is invalid since $n_1+n_2\neq n_1'+n_2'$, thus $p_tV_t\neq p_t'V_t'$

The correct way is to use the fact that the number of iodine atoms is constant, from which we get,
$$2n_1+n_2=2n_1'+n_2',$$
$$(2p_1+p_2)V_t=(2p_1'+p_2')V_t',$$
$$1.3 {\rm atm}=4p_1+2p_2=2p_1'+p_2',$$

Then you can go on by combining this with the equation you have already obtained from $K_p$ (listed in your question) and solve for $p_1'$ and $p_2'$.