How to Wire 3 baseboard Heaters with 2 Thermostats
You are correct -- just don't overstuff the box!

Pigtailing the wires to room 2 with the line-side of thermostat 1 will get you what you are after here.  However, with the thermostat and the 3 12/2s in there, that's too much stuff for many single gang boxes (20.25 in3 of box fill vs the largest standard device box in the Code being 18in3), so you'll want to use a bigger box such as a 4" square with a single gang cover/mudring there instead.  You'll also want to wrap each of the white wires in this with black tape to make it clear that they're hots, not neutrals.