Running VMware in VMware?
I've never run VMware in VMware, but I've run VirtualPC inside VirtualBox without problems, so there's no fundamental reason it shouldn't work I suppose...
It sounds to me more like you have a problem with the inflexibility of your "network czars" than any technical one. If you're a developer or QA you need a testing environment where you can fool around with outdated (and potentially insecure) versions of the OS and applications, without putting the rest of the company network at risk.
Ex-VMware employee here.
Firstly, when you say Nested VMware I will assume you mean Nested ESXi. (You could also mean Workstation, Fusion, or Player).
Nested ESXi environments are unsupported and should not be used for production. These scenarios are not tested in QA and not guaranteed to work. In short, if you experience any kind of problem, VMware will not help you with this Nested ESXi setup.
With that said, yes you can do it and yes it does work. A lot of people use nested ESXi in their labs but not in production. Previously there were special configuration file edits that were necessary for nested ESXi to work. I have seen environments with even 3 layer nested ESXi servers (ESXi vm on and ESXi vm on a physical ESXi host). More recently there is the ESXi appliance which makes this much easier.
Have a look here: http://www.virtuallyghetto.com/2015/12/deploying-nested-esxi-is-even-easier-now-with-the-esxi-virtual-appliance.html
The technical limitation with running VMware inside VMware is that VMware, Virtual PC, etc takes advantage of the Virtualization features present in modern CPUs.
If you have two or more hypervisors are both trying to control Ring 0 then there will be problems, this is something that I've encountered while trying to run both VMware and Virtual PC simultaneously on my desktop - one will error out/crash.
If your hypervisor can interact with the 'parent' hypervisor, then you'll be OK. Alternatively if the child hypervisor doesn't try to use the CPU virtualization features, or entirely emulates the CPU (such as QEMU) then you should also be OK.
Basically old-style hypervisors on old CPUs use Full virtualization (slow) which would be capable of nesting with a heavy, heavy performance hit. modern Hypervisors/CPUs use hardware assisted virtualization (near native performance) and you'd be hard pressed to find a hypervisor that is designed or capable of nested virtual machines.
Finally, I'd really advise against running dev/test VMs on the same physical server that is running production VMs. There's just too much to go wrong and security implications - you need to manage the dev/test environment and it sounds like you shouldn't have access to production environment. Likewise you probably don't want the operations team messing about with your test environment.
UPDATE: ESXi 4 now supports virtualizing itself. See this article for more information
I ran into this same problem. I work at a large company where our entire infrastructure is virtual, so if you need a server you get a VMware VM. So I had a couple of Windows 2003 Server Standard Edition based Guest VM's that had 6GB of memory and 200 GB of disk space, but I wanted to run linux and a LAMP stack on them. So I tried to install VMware Workstation on one and I got an error message saying it couldn't be installed within a VM. I also tried Microsoft Virtual PC and got a similar error message. I installed Sun's VirtualBox and that installed fine, but I couldn't get the networking to work w/in the guest Ubuntu OS. My next step is to try QEMU although performance might become an issue.