I teach with VIPKid and was using ManyCam for months before I switched to OBS. I switched from ManyCam because my video feed began messing up and students told me I would "freeze" on screen for a minute sometimes. This was annoying since it was easier to use ManyCam by a good margin. Your mileage may vary and I still love ManyCam when it wants to work.
That said, to use OBS with VIPKid you will need to use OBS-VirtualCam or a similar OBS addon to create the "virtual camera" that VIPKid will be able to use (
https://obsproject.com/forum/threads/obs-virtualcam.71741/ ). There are instructions for installing and running the VirtualCam add-on once you click on the link, but I can try and help you more if you run into any issues.
As to picture-in-picture, you would need to add a second video source and then choose what item she wants to display. If that is a website then you would select your browser as a source and if it is an image then you select the image option. You will have to move and scale the objects around on the screen which can be frustrating (This is where ManyCam shines, but again may cause issues during her classes). If she doesn't want the second object (website, picture, etc) to always be on the screen, you can click the small "eye" icon which will make it disappear off of the screen until you click on the icon again. This will allow her to have multiple feeds already set-up prior to class and will only be a single click away. As a warning, watch out for the order that they are listed in the Sources column as the highest slotted one will be present over the one below it...
If she intends to use a green-screen I can help with that as well, just let me know. I am sure I have been confusing in some way but I literally just set my OBS up for VIPKid this week so I happen to still remember everything I did to have it ready. Please feel free to reply with any questions!