So I finally found that specific Plugin I mentioned above, but... yea... it has a major issue, PROBABLY. Maybe you can fix that.
but before that: i can't program, I just looked at the plugin i linked and read what notetags are available for that plugin (and hopefully somehow help solve your issue, even if it's indirectly)... so I don't know if that's possible what you're asking.
I found out somewhere in this forum that the user creating the plugin did something bad, so I don't want to link it... but if you google "rmmv yugioh field effects" you can find it.
Basically, what you can do with that plugin is: set types for your actors/pets (f.e. pets are the class "summon"), define in a skill what classes are effected (in your case "summon") and finally adds a state to those.
So you just have to define your state? hpreg for 1 turn or any settings you want to do.
Another problem that could be that the skill which gives those classes state(s) stays. Maybe you can find out how to get rid of that.
About the unlock skill problem... i srsly can't find a thing. Hope it's still useful information and you can fix your problem.

GL and cheers