2004 Mitsubishi Outlander Air conditioner works intermitten

2004 Mitsubishi Outlander 4 cyl 66000 miles

My Outlander was wrecked and part of the repair was to replace the Air conditioner clutch and pulley. The shop ended up taking out the Air compressor also and put in a combined unit of air compressor and clutch. Since then it hasn't worked properly, It will be cold for about 10 min and then blow warm. The blower does stay on. When I took it back to the shop, they said it had nothing to do with the repair they did and it was due to a dirty core, and they would need about 6 hours of labor and take the dash out to fix it. I then took, the car to the Mitsubishi place and they said that the RPMs on the part that was replaced was not correct for my car. When I went back to the repair shop they said they did put in a mitsubishi part and it has nothing to do with it. I then went to the third place to see what they thought the problem was, and they said they could see the clutch slip and the cool air switched to warm when the clutch slipped and I need a new clutch and air compressor. The original repair shop did agree to take the part out and send it out to be checked. If the problem has to do with the RPMs and my outlander, would this be found out, by sending the part out? Also, could a slipping clutch, and air that blows cold and then warm, and then cold again, be due to a dirty core? Come to find out the insurance paid them only for the clutch so not sure why they replaced the air compressor also. I appreciate any thoughts.