It appears you have multiple questions here.
For the ODBC (and others) problem with sub forms, see my answer (and subsequent links) in this post → Error message in Base: The data content could not be loaded. Invalid Descriptor index.. Don’t think Base crashes but rather an error is displayed.
Now for Base and MySQL. After reading this you may want to check for existing bug reports and file one if you feel inclined to do so here → Bugzilla.
Now prior to either v6.1.x or 6.2.x Base & MySQL worked as you stated: Connecting (displaying) to only one DB (actually in MySQL there is only one DB; all else is nothing more than multiple schema). This is when LO was changed to use MariaDB connector for SDBC connection vs the MySQL SDBC connector. This caused multiple problems for my systems and I moved to PostgreSQL dropping MySQL completely.
No you can eliminate the display of the other schema you do not want to see. From main Base screen menu select
Tools->Table Filter... and there you can remove the display of items not wanted. Once done, while in the main Base screen on the
Tables section, from the menu select
View->Refresh Tables and you should now only see what you have selected.
Only my opinion, but this could be correct either way as the MySQL container does not truly have multiple databases as say PostgreSQL does.