I understand the super node aspect of this circuit, but I'm unsure of what to do as I dont see a direct way to proceed with KCL using all of the nodes. I found the equation for the supernode, but I'm unsure of the rest.
simulate this circuit – Schematic created using CircuitLab
Supernode: 12=v1-v2
node 1: 1=v1 + ???
node 2: ???
Here's a slightly redrawn schematic.
(I'm keeping it mostly as you had it, because nodal analysis isn't about understanding a circuit's design and behavior and more about just applying a systematic mathematical approach. And it's also just an academic exercise -- the schematic isn't supposed to do anything, anyway, except pose a problem to solve using a tool.)
simulate this circuit – Schematic created using CircuitLab
I intentionally dropped the ground connections on the other side of your current sources. That connection isn't needed as current sources have \$\infty\$ impedance. I also re-labeled your two nodes to avoid confusion with \$V_2\$ in your schematic.
I've also introduced a new variable for the current in \$V_2\$. This is an unknown variable, but it will be resolved if you solve out the equations.
For each node in the schematic above, I'll list the out-flowing currents from that node on the left side of each equation and I'll list the in-flowing currents into that node on the right side of each equation. The last equation provides the final information relating node 1 and node 2, as you already know.
$$\begin{align*} \begin{array}{r} {\text{Node } 1:} \vphantom{\frac{V_{N_2}}{R_3}} \\\\ {\text{Node } 2:} \vphantom{\frac{V_{N_2}}{R_3}} \\\\ {\text{Assign}:} \vphantom{V_{N_2}+V_2} \end{array} && \overbrace{ \begin{array}{r} \frac{V_{N_1}}{R_1}+\frac{V_{N_1}}{R_3} \\\\ \frac{V_{N_2}}{R_2}+\frac{V_{N_2}}{R_3}+I_{V_2} \\\\ V_{N_1} \end{array} }^{\text{outflowing currents}} & \begin{array}{c} &\quad{=} \vphantom{\frac{V_{N_2}}{R_3}} \\\\ &\quad{=} \vphantom{\frac{V_{N_2}}{R_3}} \\\\ &\quad{=} \vphantom{V_{N_2}+V_2} \end{array} & \overbrace{ \begin{array}{l} \frac{0\:\text{V}}{R_1}+\frac{V_{N_2}}{R_3}+I_1+I_{V_2} \\\\ \frac{0\:\text{V}}{R_2}+\frac{V_{N_1}}{R_3}+I_2 \\\\ V_{N_2}+V_2 \end{array} }^{\text{inflowing currents}} \end{align*}$$
Can you solve the above for \$V_{N_1}\$, \$V_{N_2}\$, and \$I_{V_2}\$?
