For the frozen months, I have to run my sump pump hose to my laundry stack to drain. This causes significant backsplash that shoots out around the washer hose every time the sump kicks in. My stack drain pipe has a branch off the side for the sump drain and the washer hose drains in the top. I believe I CANNOT seal the washing machine drain hose into the pipe, as I've been led to believe it needs escape for air. How do I prevent this splashing soaking my laundry room every time my sump pump kicks in until spring when I can drain it outside again? Would putting a cloth inside the stack around the washer hose end inside the drain stack work to cut off the water spraying out, yet still allow air to escape?

you can cut the standpipe about 1 inch from the trap and glue on a 3 x 1 1/2 coupling. then put a 18 to 24 inch piece of 3 inch pipe. create a sort of funnel for both hoses to hang inside of..

Do you have city sewer or septic tank? If it's a septic tank don't drain your sump into it. You will cause your septic system to fail resulting in very expensive repairs. Where I live draining a sump pump into a city sewer system is illegal and can result in significant fines. If it is a city sewer and its legal to drain your sump pump into then you need a larger stand pipe to handle the volume of water from the pump .