From what I have seen when you capture/destroy the home planet of a species that has control of more than 1 planet it simply shifts the "home planet" status to another planet under that species'(sp?) control.
The only time it really matters when you capture/destroy a home planet is when it is the last planet under their control.
I'm actually doing that now. I managed to start up talks with the Grox before they starting shooting, and here's what I've found. (playing on hard, not sure if it's much easier on other difficulties)
I started out at -70 rep with them, they REALLY don't like others.
A gift of $100,000 will get you +3 rep per gift up to +10 rep from gifts max.
I then went in closer, and used the Super Happy Ray, which I was able to get a +30 rep for using friendly tools.
I then dropped an embassy, as I had a bio-disaster to prevent on one of my colonies I'll be heading back asap to do missions as well, but I was at neutral when I left for home space.