Simple version: You need a special kind of switch called a "3-way switch". Replace all your aluminum house wiring with copper ASAP.
Aluminum wire!
Aluminum small branch circuit wiring turned into a disaster in the 1970s. There were many fires. The industry did a whole lot of soul-searching and in my opinion positively identified the problems, and aluminum can be worked with safely if you follow the rules.
I didn't mention that earlier because many people don't have the skill/chops/patience to do it. You say you do? OK then.
You must use a receptacle or switch rated CO-ALR. Turns out, UL had been pressured by the government to rush the certification of switches and outlets for aluminum wire. They screwed up. When reality caught up, they issued a much tougher standard for aluminum rated receptacles/switches, this is CO-ALR. You will note that the terminals are made of a soft gray rare metal called Indium. This is compatible with aluminum wire.
Or, you must "pigtail" with Alumiconns. The selection of CO-ALR switches and receptacles is limited. If you're not satisfied with the available choices, you will need to pigtail with copper wire. In order to splice the copper to aluminum, you must use Alumiconns, which are a type of lug splice. Alumiconns are a "lug connector" just like the neutral bar in your panel. In both cases the lug body is made of aluminum (with copper, thermal expansion differences work in its favor).
You must torque terminals to spec. If it has a spec. Unrelated to aluminum wire, science showed that electricians couldn't set torques any more accurately than their spouses - and this was indicated in many terminal failures with copper wires. It explains much of the trouble with aluminum, and is a Code requirement in any case. A 1/4" beam-type torque wrench is an affordable tool with the correct range of torque.
AFCI breakers aren't a bad idea
The main failure mode of aluminum wire is to have a loose connection and start arcing. Arc Fault breakers are able to detect this, so they provide "belt and suspenders" in combination with the above.
3-way circuits require 3-way switches
Here's how a 3-way circuit works.
(Black is always-hot, yellow are travelers, red is switched-hot. Of course everyone just uses the standard cable colors, so you have to figure it out.)
As you can see, it isn't going to work with switches that have only 2 terminals.
Green is for safety ground only, but you don't need to worry about wiring ground, as the switch will pick it up from the steel box via its mounting screws. Nice thing about metal boxes!
You seem to have identified the travelers perfectly well, so you have it on the run. You just need the right switch. That is CO-ALR. (or pigtail with Alumiconns).
Um, yeah, the rest of your house may need attention
It's rare to have aluminum wires on just one switch leg. It's likely your house will need to have many if not all switches and receptacles replaced with CO-ALR types (or pigtailed with Alumiconns).
By the way, there is another permitted method called a COPALUM splice. An idiot could buy those crimps and use a common hand tool, but to work properly they need an expensive hydraulic crimper that applies 10,000 pounds of pressure to effectively do a weld. The crimpers are VERY costly and hard to find.
The "Purple wire nuts" do not work, and there are plenty of photos of burned up purple wire nuts on the web. In fact if you google "burned up alumiconns" you don't find any of those, but you find pictures of purple wire nuts.
