I just had a similar problem with my 97 camaro 4l60e tranny. I got the same code as you except my first to second shift felt like I had been rear-ended. After getting a transmission shop to look at it, it required a rebuild. My torch converter and overdrive band were bad along with my tranny mounts. I had them rebuild the tranny for about $1500 bucks. They replaced both items above and installed a Superior technology shift kit (
http://www.supersportperformance.com/4thgenfbody.htm)to eliminate the 1870 code. You can also look at Transgo shift kits(
http://www.transgoperformance.com), I have been told both are good. I have had my car back for about 3 days now and have only put about 60 miles on it but the improvement is monumental. Good luck with your repair.