I want to do that using a code and not using a tool like \"MySQL Migration Toolkit\". The easiest way I know is to open a connection (using MySQL connectors) to DB1 and read
You can use mysqldump and mysql (the command line client). These are command line tools and in the question you write you don't want to use them, but still using them (even by running them from your code) is the easiest way; mysqldump solves a lot of problems.
You can make selects from one database and insert to the other, which is pretty easy. But if you need also to transfer the database schema (create tables etc.), it gets little bit more complicated, which is the reason I recommend mysqldump. But lot of PHP-MySQL-admin tools also does this, so you can use them or look at their code.
Or maybe you can use MySQL replication.