Wouldn't the amount of divergence be completely in relation to the ease in which the changes could be enacted? Lower classes attempting to acheive higher status would simply do what they could to "look" upper class - at the very least to ease any chance of mobility. We do this now with hair, teeth, skin etc. It's not a surprise that a stereo-typical hick is missing teeth and looks dirty.
Currently we can't easily genetically distinguish between the rich and the poor - instead we adopt trappings that give us cues. Genetic changes would be very expensive at first (like good food and clothing was 200 years ago), and the rich would use it (think Sleepless by Nancy Kress) to gain an edge, maintain the status quo. I suspect there would eventually be breakthroughs that would make it more cost-effective, though.
What effects would birth rate have? Would the culture with the longer life span wait until later in life to have children?
I suppose in rich countries we have that now to a certain extent - but I don't really have an answer, just a comment that a friend of mine used to make that smart people need to have more children. At the current rate, he'd say, the welfare crowd is going to eventually seriously outnumber all the rest and society would be in trouble.
Consistently removing "the best" from one group would lessen the chance of creating more, would it not?
If the "best" move out of a group, what traits would be valued by that group, then?
The first question doesn't hold. Objectively it would be like any stock - all things being equal, as long as you didn't pull out more than was being made, it could go on forever.
As for the second question, we see the answer today. If the goal is to escape the "worst" group then the traits of the "best" group are desired (studying, saving for college, getting a good job). If the goal to to remain in the "worst" group (or to be fully aware of no real chance to escape it) then it's more about survival. And you would see a dicotomy of values in those two sub-groups.
I question a serious divergence from ever really happening. Isn't it proven to be self destructive when doing this? Think about the inbreeding of many royal families (Egyptian, Japanese, European, etc.) this seems to lead to eventual ruination.
I suppose if there was a large separation (another planet as wintermute suggested) then over time we would see enviromental factors take over but only if they were lacking the technology to correct "abnormalities". I've read articles about the death of the Deaf culture because of cochlear implants. This can be considered an example of a divergence brought back to the mainline.