David,
First, I'm very sorry for the delayed response!
Right now, the SocialShare module does include the individual 'tags' for the LinkedIn, Twitter, Google and Facebook buttons. Those tags look like:
{JLinkedShare}{SCTwitterShare}{SCGooglePlusOne}{JFBCLike}
I can imagine that those could cause some conflicts if they are included inside another tag.
We are planning a new way of creating that module (and our others) that will directly load the HTML instead of inserting the tags which are then translated. It should make things (slightly) faster, but also less complex. That should be a part of the v5.3 release due out in early 2014.
Until then, my suggestions would be:
* Use the 'raw' tags above, instead of trying to load the module in the content. It's less flexible as you won't have the easy parameter settings from the module, but should just work.
* Try re-arranging the ModulesAnywhere plugin to be ordered before and/or after the JFBCSystem plugin. That may help fix the rendering issue, but I'm not sure it will help.
I hope that helps get you started and going in the right direction with some options. Again, hopefully the next major release will fix this up completely.
Thanks,
Alex