I’m looking for some help on a frozen washing machine drain pipe. Any assistance would be greatly appreciated. First the facts:

1a. I am not a plumber and I apologize in advance for any dumb sounding facts below
1. My wife and I had a 2nd story addition put above our garage about a year ago which included a master suite and moving our washer and dryer from the basement to the 2nd floor (great advantage).
2. The washing machine drains into the same main drain pipe as the bathtub, sinks, toilet, etc
2a. The drain pipe sits on an outside wall
3. About a month ago we had the drain pipe back up and called a plumber out. He told us the trap was probably frozen. He was able to auger through the ice but told me that if I kept pouring hot water into the pipe and shopvacumming it out I eventually fix it.
4. We live in Upstate Ny and today we had the backup again. None of the other fixtures have the problem so I believe the trap to frozen again
5. Not wanting to shell out $200 again I bought a snake myself from the hardware store. I did the hot water trick for at least an hr as well as having a heater blowing directly on the wall and no progress.

Now to my question :) - When I pull the snake back out of the pipe (goes about 3-4 ft) its cold and clean - which further leads to the ice theory. However - my concern is - is it possible that the top of the trap has a flapper on it? When I feed the snake into the pipe it always stops at the same spot - which sounds like metal on metal and it almost feels as if I can push on one side and raise the other.

Is it possible this isn’t an ice problem but a poor plumbing problem? This addition is less than a year old and I don’t want to worry about this every winter (its cold a lot in Upstate NY) plus should I be concerned at the PVC bursting with all the expansion and contraction?

Any and all responses are greatly appreciated.