Start/stop Windows Service A also Start/stop Windows service B

"Real" service programs have code to handle performing cleanup and shutdown activities. You're running a program that wasn't intended to be run as a service, and it has no such code to handle graceful termination when the Service Control Manager (SCM) signals that the service is stopping.

Somebody could write a nice service wrapper for VirtualBox that could gracefully handle running as a service. That's the real solution. Unfortunately, you're not going to come up with a "hack" that will do what you're looking for. SRVANY (and every other program of the same type that I'm aware of) doesn't have any capability to execute user-specified code when SCM signals that the service is stopping.

Find out the existing dependencies, add your new one and write the whole thing back, say you have a service called w3svc, you can use:

sc.exe  qc  w3svc

or in PowerShell:

(get-service w3svc | Select ServicesDependedOn).ServicesDependedOn

where you can loop through these and build a new sc.exe command to execute.

Example:

 $serviceName = "w3svc"
 $cmd = "config $serviceName depend= "
 (gsv $serviceName | Select ServicesDependedOn).ServicesDependedOn | % {$cmd += $_.Name + "/"}
 $cmd += "myMasterService"
 invoke-expression "sc.exe $cmd"

We are building a command string from the existing services and add your own.

To remove yours do the same thing, but in the loop exclude your service.

 $serviceName = "w3svc"
 $cmd = "config $serviceName depend= "
 (gsv $serviceName | Select ServicesDependedOn).ServicesDependedOn | % {
      if ($_.Name -ne "myMasterService")
      {
           $cmd += $_.Name + "/"
      }
 }
 # remove the last slash
 $cmd = $cmd -replace "/$", ""   
 invoke-expression "sc.exe $cmd"

I haven't tested the actual sc.exe commands, but I assume you know what you are doing.