Don't take this the wrong way.
The absolute best way to get around this problem is to create primary keys on all of your tables.
SQLYog provides a nice front end for you to edit but on the back end it's simply issuing UPDATE statements. To issue an update, SQLYog HAS to have a way of identifying the exact record you want to update. Without a primary or a candidate (UNIQUE) key, there is no way to do this.
phpMyAdmin is a toy for those who don't know how to use better tools. (IMHO) Yes, it allows you to do this…and yes, if you have 2 records exactly the same, it will update them both when you edit one. Nature of the beast.
HTH,
=C=