"Yes ma'am, I will."
She can let herself out, then. And - think. She feels like she did in fact learn something, but like whatever she learned was probably not relevant to rescuing Elie at all. If she'd had to pay up front she might be upset with herself about that, but she didn't, so it's fine, really. She'll make it all up in a week or two, if she survives whatever plan she comes up with.
She turns it over and over in her head. She can't think of a way to navigate the ocean effectively enough to catch the ship, no matter what method of catching up she tries, and she probably won't be able to tell what port the ship is going to until morning, at which point catching up will be a lost cause. Catherine almost definitely can't make it in time, and whatever is going on with Shawil right now, he certainly can't be relied on. So -
She has to determine what port it is. It will not be safe to do this until morning, if she doesn't want to get arrested (and she doesn't know exactly how she would go about ceasing to be arrested, not having any available male family members who can interface with the legal system for her). That means - she should refine the plan in which she teleports to the relevant port city, finds Elie before he can be unloaded and executed, and then teleports out. She will need to find someone who can teleport to the city in question. She will need to think of a way to avoid detection while she's there. Maybe she can get some Chelish clothes and sit and watch the docks while looking like an old woman? That sounds risky, but she doesn't have a better idea. And then when the ship comes in she can turn into a dragonfly and fly out to meet it, and search for Elie while she's still a bug, and hopefully find him before the ship even lands, and then as soon as she falls out of dragonfly form she should be able to teleport both of them back to Sothis.
She hopes she's able to get into her accounts. She's never tried to withdraw money without Shawil there, and it's a lot of money, and - well, she has to try.
She feels kind of bad about leaving Rahim with the church all night. She doesn't think anything bad will happen to him, but it's - not being a good mother. But sometimes other things are more important than being a perfect mother. She'll come get him after. She also feels kind of bad about leaving Wishbone alone all night, but Wishbone will understand, probably.
She spends the night at the temple, praying to Nethys and thinking about refinements to her plan. Shawil does not show up. At first light she heads home, prepares her spells, and then heads off to the temple of Abadar, where she will wait in line and then ask the person at the desk whether they know where she would be able to get records of which ships have left the harbor in the past day.