Madeline's client wants her on site to get the dimensions exactly right. This is fine. Perfectly normal, even. It's rare when someone pays her knowing exactly what they want her to make. If they did, why would they even want to hire a conjurer, whose creations can be changed and edited easily. Except getting to this site involves a two hour plane ride and a hotel room in some middle of nowhere town. This moves things from 'normal' into the territory of 'a massive pain,' involving getting plane tickets, and waving her conjuration registry at airport staff to confirm that she will be bringing her familiar with her on the plane, and sorting out a hotel room and keeping all of the receipts so she can file the whole as a work expense for taxes, and packing, and getting her baggage checked, and finding the right gate at the airport and and.
At least she's being well paid for this headache. She kind of needed to get out more, anyway.
Her (singular) bag is given over to the care of airport staff, and cat and carryon (containing sketchbook, drawing supplies, phone and charger, a change of clothes and some deodorant in case her main bag gets lost) are kept with her. A normal animal would need to be in a carrier, but with a familiar that would be kind of silly. Instead she'll be tucked away in their creation space, which is comfy and warm and metaphysically situated right next to Madeline's heart. This is much preferable to a picky kitty than a carrier. Also preferable to Madeline herself, who can feel her picky kitty nestled away, safe and cozy and snoring gently, far away from the bustle and crowds of the airport. She might get a lapcat partway through the plane ride, but bringing her out here would be downright cruel. Tempest would find it overwhelming and flee immediately, either into their creation space or into a dark and no doubt impossible to reach corner somewhere, depending on how mad she was at Madeline.
She does kind of wish she could have a lapcat while waiting for her plane to start boarding, though. Her familiar tucked away by her heart and distanced from the bustle of the real world is comforting and all, but there's no warm fluffy thing that loves her available to pet. Terrible. The conjurer checks the time on her phone, then gives an unhappy huff and leans her head back on her (uncomfortable) airport waiting chair. Nope. Not boarding yet. Still going to be surrounded by crowds for at least another ten minutes. Yaaaaaaay.
And then it feels like her chair disappears out from under her, and she gives a little yelp, and she's somewhere else.