while it would be possible, I will suggest to do both windows with a Vulkan API backend in the same process. Vulkan was made for advanced usage patterns like this. The major problem I see is that all the advantages of using Vulkan API (low level control over the GPU) are given up by using OpenGL next to it. This could not only decrease performance, but also bring up some strange driver behaviour issues, as OpenGL drivers do a lot more guesswork and it’s much harder to predict what will happen. The worst case would be that your app is running on your machine, but does not run at all on other machines due to these issues.
Vulkan API on the other hand offers you all the low level control you need: If the user has 2 graphics cards, you could use one for each window for example. If not, you could coordinate your rendering much better with Vulkan than with a mixture of Vulkan and OpenGL.
As far as I know, Vulkan was not really made to be coordinated with OpenGL which means it contains no functions which could solve some of these complex driver issues. Correct me if I’m wrong. Same applies for OpenGL: It is not made to be coordinated with Vulkan API.