The Washing Machine Overflows While Draining

I've seen this problem asked a few times before and I'm unclear about which situation my resembles and which direction I should take.

The Machine Drain overflowed for the first time yesterday. There had been some gurgling for a while and I think this situation has been brewing for awhile.

The machine drains into a PVC pipe about 4 feet high. The tube is just placed into the pipe. The pipe is not air sealed at the top. The pipe dips into the crawl space, then travels under the floor. About 12 feet later the kitchen sink hooks in.

When running the sink, I can hear gurgling coming from the washing machine pipe. When the washing machine runs, it sometimes overflows into the kitchen sink.

. . . back under the floor. After the intersection of the sink and washing machine, the drain turns downward and goes underground.

On the outside of the house, there is PVC pipe coming from the ground. It protrudes a few inches. and the top has some holes drilled in. I imagine that this is a vent. I don't see any connection with this vent and the sink - nor with anything else. Spatially, it is very close to toilet and upstairs plumbing light and farther from the 1st floor plumbing (kitchen and washing machine). But one possibility is that the recent snow and freezing weather has plugged up the vent. There is no problem with the drainage upstairs. The drainage in the kitchen sink is adequate, except for the gurgling sounds.

So in order of importance:
How do I prevent the overflow of water at the drain?
How do I prevent water from backing up into the sink when running the washing machine?
How do I quiet down the gurgling?

Thanks, Michael

ballengerb1

Ah duct tape, the magic that repaired many things in my earlier life. I never go anywhere without a hefty roll, comes in colors too.

Michael9999

I primed and glued the loose pipe. Everything is good now. Washing machine ran with no water overflows or leaks. Thanks!