You want a type-1 hypervisor
From the way you describe the scenario, it sounds like you want a type-1 hypervisor specifically:
(image CC0 by Scsami)
That is, sitting above an OS.
Windows Server with Hyper-V and Desktop roles
To fulfil your requirements of having a type-1 hypervisor and being able to run and switch between Windows and Linux (some flavours thereof), running Windows Server (eg Server 2016) with the
Desktop experience roles should let you manage them locally via console.
There is more information on Hyper-V available on its overview page:
Hyper-V is Microsoft's hardware virtualization product. It lets you create and run a software version of a computer, called a virtual machine. Each virtual machine acts like a complete computer, running an operating system and programs. When you need computing resources, virtual machines give you more flexibility, help save time and money, and are a more efficient way to use hardware than just running one operating system on physical hardware.
And it does support Linux (and FreeBSD) as well.
(Side note: the question of Hyper-V being type-1 has been raised and answered over on Server Fault)
If you use an additional GPU, you could use Xen
Using an eGPU (like one added via USB, for example) would let you pass through one graphics card to a guest (
DomU, in Xen parlance) and retain the other to access the OS (
Xen 4.0.0 is the first version to support VGA graphics adapter passthrough to Xen HVM (fully virtualized) guests. This means you can give HVM guest full and direct control of the graphics adapter, making it possible to have high performance full 3D and video acceleration in a virtual machine.
but note that your laptop must support this:
Xen VGA passthrough requires IOMMU (Intel VT-d) support from the motherboard chipset, from the motherboard BIOS and from Xen. Please see the VTdHowTo wiki page for more information about Xen VT-d support and supported chipsets with IOMMU.
Xen does support Windows as a DomU (see under 'Windows 7/XP/Vista/Server 2008'), and has a FAQ on drivers which may be worth reading if you go down this route.