Wash Machine Drain problem

I've been having problems over the years of water going down the drain for my wash machine. My house was built in the late 50's or early 60's and has 1 1/2" galvanized pipe for the drain. I have had it "augered" out one other time a few years ago and checked for water flow, but I'm suspecting I need to replace it with pvc. The problem is that my wash room is setting on a cement slab that was built on with an addition to my house at some point in time. I can actually see under part of the slab from my crawl space. The vent for the washer is tied into the pipe under the slab (into a "trap"); it goes up the wall exposed, then 90's into the wall, then out the roof. I figure the only way for me to replace it would be to cut out part of the cement where the old pipe comes up, tear out the old stuff and replace with new. I'm not a plumber, I'm actually an electrician( I hope you don't hold that against me But I guess, since everything is exposed coming out of the cement, it would be best to set a surface mount box, then run my new drain out the bottom and run a new vent through a trap, back through the roof. Wonder if someone might be able to give me a few pointers on how to do this? Right now everytime the wash machine goes into a spin cycle, the water backs up and spews out the drain pipe. My wife is having to put towels up there to soak up some of the water.
She's actually been very patient, but something certainly needs to be done. Can you help me out? Thanks a lot...

I suspect it is the 1-1/2" drain that is causing the problem. Newer washers pump out wash much faster than the old ones and require a 2" drain. Of course the drain always requires a P trap and vent.

Also having the trap and vent under the slab makes me think it is an incorrect installation and something that shouldn't be copied.

The p-trap should be above the floor and the standpipe has code requirements as to minimum and maximum length. It also has to be above the water level in the machine. The vent should tie in after the trap before it turns downward through the floor. Have you got any turd herder buddies that could give you an on site consult?

Thanks for the replies. We did have to buy a new washer about 6 months ago. I sort of suspected this might be adding to the problem. We had the problem before the new washer, but it had been quiet a while since we had been having problem with it. Actually I thought we had fixed it a while back, but I guess the stronger pump on the new washer, plus the old 1 1/2 drain together, magnified the problem. I have a friend who might be able to give me some "on site" advise as how to go about changing the drain to 2". It goes down the wall under the slab, where the "trap" is located, then goes about 6 ft. horizontal til it gets under the crawl space, then it is ninetied(?)
down at a 45 degree angle to the outside crawl space wall, then goes on the ground about 10 ft. before it slopes down and ties into the sewer drain. Quiet a few turns and 90's. I guess it's a wonder how it's drained all these years. Looks like it's going to be quiet a job replacing. I'm sure I'll have to get some more input and probably some help before tackling this. I just want to have everything together( parts etc. ) before I start. Thanks again for the input though

Before replacing u may want to try power jetting the line. This cleans the entire inside of the pipe and that is probably the problem as galvanized pipes tend to get alot of build up over the years.

As a temporary "fix" while you decide what is best, you might try draining the washer into a utility sink that can hold what the drain is slow to handle.