Does electrolysis of aqueous tin(II) chloride produce Cl₂, SnCl₄ or both?
Let's try to look at those electrons. C - cathode, A - anode. 

$$
\begin{align}
&amp;\mathrm{C(-):} &amp;\ce{Sn^2+ + 2e- &amp;→ Sn^0} \\
&amp;\mathrm{A(+):} &amp;\ce{2Cl^- &amp;→ Cl2^0 + 2e-}
\end{align}
$$

So, your second reaction is right. But the first is wrong: $\ce{Sn}$ is reduced, but there are no oxidation. You should use 

$$\ce{Sn + 2 Cl2 → SnCl4}$$

But I should mention that this reaction is for $\pu{115 °C}$, so don't worry, it won't go for your conditions. 

Another way is

$$\ce{SnCl2 + Cl2 → SnCl4}$$

It requires a lot of work, bubbling $\ce{Cl2}$ through aqueous solution and distillation in the end, so you also shouldn't worry. 

You can basically think that all you $\ce{Sn}$ that becomes a part of new structure goes into solid $\ce{Sn}$. It's acceptable since synthesis of $\ce{SnCl4}$ is not an easy thing.