Odd set up

My wife and I just recently bought a house. The previous owners remodled the kitchen. When they did this they expanded the kitchen into the laundry room and moved the laundry room out into the garage.
This is where it gets fun!!! There are no sewer lines out in the garage and the house is on a slab foundation. So that makes no where for the washing machine to drain to. The way they solved this problem is by letting the washing machine drain into a trash can then pump it out with a sump pump. The water then leaves the trash can (via a pvc pipe) goes up into the attic then back into the kitchen. This leads to the line freezing in the winter time and various other problems.
So now here is the question. I would like to make it so that the washing machine drains directly into the sewer. My plan is to cut the concrete in the slab. Run a new line out to the sewer line that is in the front yard. Does this sound like a good way to fix this? If so how would I locate the line in the front yard?
Thanks in advance for your help.

Find the clean out outside, or if there is a crawl space, go into it and find it's exit point, and yes you are on the right path to fix this. Don't forget to vent it at the closest wall before you connect to the mainline outside.

Laundry line size is 2"

Good Luck, Ron