Single MySQL DB contains both push and pull data. Recommended path to replication?
You may set up a Master-Master-Replication in which both servers are slave of each other and one can write to both servers.

If you always make changes to just one subset of the tables on each of the servers, you do not run into problems concerning auto increment values (you might want to set auto_increment_increment and auto_increment_offset anyhow) or simultaneous writes to the same data on different servers.

But please note that a Master-Master-Replication can result in severe chaos, if one does something wrong.

Actually I do not understand why you do not fill the product tables in the production directly and not in the development database? You then could use one single master for writes and just keep a slave for backups and statistics / analytics, which want current data, but do not need the latest at all time. Makes configuration, maintenance and failure resistance a lot easier.
That is the solution I would prefer in this case.