Why would they mind? Since mc going on a journey is a foregone conclusion, them "not wanting to go on a journey" is equivalent to say "don't want to go on a journey to the extent they rather not have their daughter in their life if it means they have to journey".
Add to that how they have literally nothing in that area they enjoy, and only painful memories from the debt situation + forced hard work, and enemies.
Finally, as fugitives, it should be easier to flee persecution if they go on a journey, than if they remain in a location that elf-girl might have drawn attention to by visiting and publicly taking actions against a noble.
They have long af lifespan, her going on a journey is like a kid going to the kindergarten for a day. If mom doesn't go then dad won't either (although poor dad probably won't see adult Reni unless she come home for a visit). You are making this more harder and dramatic than it actually is, it's just a simple whether they want to go or not, and if not then they're not coming. They knew their daughter is special and there's nothing to worry about, and the only problem they have is going to be solved soon by Reni anyway.
Samyuu is coming with Reni so your last worry is a non-issue; them dealing with the nobles publicly is only conjecture for now (I doubt they are that stupid). Not to mention it's the parents' dream to live a peaceful life and settle down, they were
doing just fine before they got targeted by the mayor.
Not that I can't see where you're coming from, but rather than coming with her on a journey, they could've just move and find some other place with Reni's unlimited funds if living in their current place is that infeasible.