I just checked, and profiles are available on iOS. Assuming you can get profiles working, this is what you would do.
First test that in your newly created second profile you can install a further instance of Blink. If profiles works like it does on Android, this will run in a completely separate environment. It is almost exactly like it being on a different device. If you can log in to Blink on this “profile device”, and get notifications twice for any event, one from each profile, you can continue.
Delete all the sync modules and cameras that you do not want your neighbour to see. Leaving her only with your existing credentials, seeing only what you want her to see. These will be the only things remaining on that account.
Now register a new account in the new profile instance of Blink. Obviously you will need a second email account to do this.
When done, log into that instance of Blink, and add the cameras and sync modules that you have taken with you to the hotel, or wherever. The ones that you deleted from your first account.
These are now on a different account and cannot be seen by her, but they can be seen by you by opening your new profile on the iphone.
Notifications from both accounts will come to your phone, and if you select a notification from your new profile, your phone should jump to that profile, run the appropriate instance of Blink, and show you the video/view you require.
Try it, if not happy, put it all back as it was, by deleting the devices in question from your new profile, and add them back in to your main profile, and you will be back to how you were.
On Android it works perfectly, so I expect the same from iOS.