Throwing a tantrum and denying the royal family because someone left the family would never be accepted. This sort of action would result in the current head being replaced.
The Rainfords have plenty of plausible deniability, at least for now. Regardless of whether they know the king of Pansylvania is compromised or not, to all outside observers it would just look like they're disputing Stroheim's assessment of Akira's magical prowess, and potentially his claim of the Rainford name. Considering Stroheim's reputation of not being any good at magic vs the Rainfords' reputation of being the best at it, there's little reason for other nations to question it.
Rainfords have dominion over this forest and purported expertise in matters regarding it, so if they say it's too dangerous even for royalty, they have the last word. Because sometimes protecting the royalty from themselves is more important than protecting their egos.
These ignorant of his achievements and current political state of the country actions would require swift corrections as they pose a risk of justifying a coalition of other nations declaring war as retaliation.
Other nations aren't likely to back Stroheim over this, because none of them have really confirmed Akira's purported achievements. Aside from the king of Pansylvania who isn't going to be broadcasting the fact that he tried to assassinate Akira and Medis and the one woman who tried to seduce Akira at the conference and got seduced by him instead, no one else of any real authority outside of Stroheim has much of a reason to believe Akira and therefore Stroheim are as strong as they say.
And even all of the above aside, Elysion used to be its own kingdom and is acknowledged as semi-autonomous, as stated in ch 164. Presumably all the other nations would know this and therefore expect the Rainfords to occasionally backtalk Pansylvania when it comes to matters of their own territory that they would know better.