How can coupled databases be kept in sync with selective uni-directional syncing and with connections that can be off for days?
The requirement that the setup has to cope with several days of broken network connections effectively rules out "virtually" synchronous multi-master solutions like Galera and MySQL group replication. And you can also forget about MySQL NDB Cluster.

However, I think an asynchronous MariaDB or MySQL solution could do what you need, assuming the binlogs are large enough to hold the data accumulated while the network connections are down. 

It seems like asynchronous MariaDB / MySQL master-master replication might be able to do what you need. Master-master replication is basically two instances of master-slave replication, where each server is master in one of the replication connections, and slave in the other. In addition it's common to have auto_increment_increment = 2 on both servers, auto_increment_offset = 1 on the first server and auto_increment_offset = 2 on the other. This way, neither database server causes collisions when using the auto_increment feature of the primary keys in INSERT statements. This will also eliminate any need for sharding in your use case.   

So you will need to setup master-master replication between your Central DB and Remote DB1, and separate master-master replication between your Central DB and Remote DB2. 

You will further need to set replicate-do-table=foo so that only that table is replicated to Remote DB1 and Remote DB2 from Central DB. And similarly, replicate-do-table=bar so that only that table is replicated from Remote DB1 to Central DB, and from Remote DB2 to Central DB. 

There are many more details, such as GTID (which is a feature which was not available initially, but is a good idea now), but here I suggest you look at the available documentation elsewhere, e.g.:

Simple Master-Master replication on MariaDB (tunnelix.com)

How to Setup MySQL Master-Master Replication (howtoforge.com)