I (British citizen) am planning a family trip with my parents (non-EU citizens/ UK residents with BRP and ILR) to Europe (country undecided) this summer. Both of them are in full-time employment, however, I am going to be fully financing this trip as their anniversary present. Neither of them have ever applied for a Schengen visa before.
I have researched on various forums but cannot figure out whether this removes the need for them to provide their employment documentation. My mother works in the service industry with a hopelessly non-existent HR system (for eg, she persistently requested for a proof of employment letter to sponsor my grandfather's tourist visa to the UK last summer and it never materialised leading us to change the sponsor to someone else (me)

I have a stable job and good financial means to cover the costs of the trip. Would a cover letter / my bank statements from me suffice in supporting the application for my parents? Can I accompany them at the appointment?
As a test, I emailed these questions to the Greek consulate but received a reply which did not even address the question! I am yet to email other consulates but hoping someone with a similar experience here might be able to provide an insight?
Thank you
