Rehearse the stay before it is a long one
A cat dropped at a relative's house for three weeks with no rehearsal is being asked to handle a new territory, new people rhythms and your disappearance all at once. Build up to it: short visits where you stay too, then a single overnight, then a weekend, so the house, its smells and its hiding places become familiar while you are still the reassuring constant. Leave her there for brief periods during those visits so your leaving and returning becomes ordinary. By the real trip, she should already have a chosen sleeping spot and a room she considers hers in that house.
Set up her territory inside their home
Claim one quiet room as her base, set up exactly as she will use it for the stay: tray, water, food station, scratching post, and her own bedding and toys from home, unwashed. Show your family where she hides when she wants out of company, and agree that she is never dragged out for visitors, children or photographs. If the household has its own pets, plan a proper gradual introduction with doors and scent swapping rather than a first-night free-for-all, and define in advance which rooms stay hers alone for the whole stay, no exceptions.
Hand over the real routine, including the awkward parts
Write the routine as your family will actually live it: feeding times and amounts, how her food is stored, the tray routine, and the behaviours that are normal for her, from dawn wakefulness to the particular chair she will certainly scratch. Be honest about costs and mess, provide ample food, litter and supplies for the entire stay plus a margin, and agree how updates will come, such as a photo every couple of days rather than anxious daily reporting. Long stays strain goodwill when expectations stay unspoken, so say the awkward things kindly and early, before anyone is tired.
Cover health and emergencies for your absence properly
Tell your vet she will be staying elsewhere, ask about authorising your family to bring her in, and leave written consent, her insurance or payment arrangements, and clear guidance on what decisions they may make if you are unreachable across time zones. Note her normal appetite and weight, any ongoing care tasks with their exact rhythm, and the signs that should trigger a vet call rather than a wait-and-see. A long work trip guarantees at least one judgement call will be needed, and your family should never have to guess what you would want done.
Keep one shared version of her care
Over weeks, small changes creep in: a different feeding time here, a new favourite spot there, a meal skipped and forgotten. One shared record that your family updates and you can glance at from the hotel keeps everyone working from the same facts and gives you a true picture when you return. Sharing her profile and care details through KinsLe Family Sharing means your family see the same routine, vet contacts and notes you left, and can update them in one place.