Trouble with three way switches
First, don’t experiment i.e. trying random stuff “to see if that fixes it”.  There are lots of combinations that will work and will kill you.
Second, you are quite close on identifying the wire’s operational roles.  They are:

Hot from supply (always measures hot)
Onward power to other points of use
Switched power to the light

If the first and second are connected, then the rest of your house will work.  And they should always be connected no matter what you do.
What’s driving you up the wall is that you are continuing a sloppy practice someone else started, which is using the switch itself as a junction block for unrelated things.  (I.e. the connection between supply and onward).
Very few switches even have provision for 2 wires on the line screw; that generally forces you into using a “backstab”, which is a bad idea all around.
You may be better off obtaining wire, nuts and the other kit required to make this a pigtail connection: join the two important wires (supply and onward) under a wire nut, so you are not using the switch as a splice, and then have a third short wire hop from the splice to the switch.  This will also make the circuit more understandable for the next person.  (Who might be you!)
I pigtail most of my stuff for a different reason, most of my connections are in awkward locations. It is easier to pigtail the outlet on a bench, then at the box simply whip together supply, onward and pigtail with a wire nut.