There should be no connection between the front shifting and rear shifting, unless you're inadvertently shifting the right shifter when you move the left shifter, but that's unlikely to be a consistent problem. A too-short chain is unlikely to be an issue - when you think about it, dropping to the small chainring would actually alleviate any short-chain issues. The only other thing I can think of - are your derailleur cables crossed over underneath the downtube? Is it possible that, by slackening your FD cable, you're introducing slack into your RD cable and causing the RD to shift to a smaller sprocket?