I'm sorry, but when Freedom showed up in a recent episode, Shinn didn't say: "OMG, the Mobile suit that killed my parents!" In fact, I don't think he even recognized it.
Also, during that one flashback episode that focused on Shinn's life, they did an edit that I thought was intersting. Before we always seen the Freedom and the other mobile suit firing at the same time, then the huge explosion that killed Shinn's family. But during this flashback they didn't show Freedom firing at all.
The only reason why Kira and Shinn will fight is because:
1) Dullindal orders them to destroy the Archangel.
OR
2) Shinn is angry at Freedom's interference at the battle that killed Heine, and probaly will be angry because he is interfering again in the battle in the upcoming episode.
OR
3) Kira interfering some other ways.