Video call integration for website and platform

Project Brief:
We are looking for an engineer that has experience working with React and Firebase. The project requires a video call function and our current solution (agora) seems to have compatibility issues and connection troubles.

Our idea is to integrate (preferably) Skype into the platform. How we are thinking of achieving this is by adding a popup window/toolbar that appears from within our platform and requires the user to log in via the toolbar and popup.
However, they would never be taken to an external page and would be able to connect to the other user who they are contacting from our front end.

This is a bit of a workaround we are looking for, so someone who has experience producing something similar would be a perfect fit. Other suggestions or workarounds would be welcomed, however, the video chat needs to be a major provider that has ironed out the bugs of webrtc, so that connectivity and compatibility are not issues.

If you are interested please contact me and we can discuss this further.

Regards,
Luke