Transmission Revs up between 2nd n 3rd

Bought the 03 Monte used unaware that the motor had been been replaced with a motor from a 1999 vehicle. I knew nothing about cars but have learned plenty dealing with this nightmare. I had a used tranny put into the car about 6 months ago when, while driving. Barely. I heard a loud cracking sound & within minutes lost all my tranny fluid & before I could pull the car over my radiator started to overheat & out came all my coolant as well! I have never seen so much fluid dump from a vehicle so fast in my 44yrs. I was dumbfounded! As I looked to see what happened I noticed the fluid had come out the sides of my tranny pan and a dent was pushed into the pan from inside the pan. After pulling my pan off I could see that one of the bolts actual blew out with such force it dented the oil pan. I knew then I had a big problem. Still not sure what caused my radiator to crack immediately after my tranny blew, but it did on the right side (driver side.)
I put a new radiator in myself & assisted a friend to put in a used tranny we pulled from a junked Impala. At this point I was unaware that the motor was not the original motor and got a 4T65E tranny that the car is suppose to have in it. I didn't realize then that the 2003 motor is year specific to this transmission, which leads me to my questions. Is my tranny going out due to the change in year of the motor to a '99? Is the missing of 2nd gear that makes it seem like the engine revs up yet bogs down at the same time, something I can fix? The tranny also seems to have a hard time knowing when to go from 3rd to 4th gear as well. Is this all related to the same issue? Can I make this tranny work w this motor or am I looking at replacing both? Please help!