As the Visual Studio integration seems pretty important to you I would suggest looking into Visual Studio Online, which has the following to say about it self:
It’s not an IDE, it’s everything else. Visual Studio Online provides a set of cloud-powered collaboration tools that work with your existing IDE or editor, so your team can work effectively on software projects of all shapes and sizes.
Idea to app – Includes code repositories, continuous integration, bug and task tracking and agile planning tools
Any tool – Use Visual Studio, Eclipse, or your own IDE or code editor
Free to start – Priced to be small team friendly. 5 users FREE, unlimited private repos
Version control – Unlimited, private, secure
Store and collaborate on code anywhere with private team projects backed by version control. Use Team Foundation version control (TFVC) for one massively scalable repo, or multiple Git repositories for maximum flexibility.
Tools for agile teams – Kanban, Scrum, dashboards
Be agile, on your terms. Capture, prioritize, and track work with backlogs and customizable Kanban boards. Work items link directly to code to ensure transparency, and can be used to build rich dashboards for easy reporting.
Meeting your requirements
It does boost of a tight integration with Visual Studio, and it seems possible to even link in stuff like TeamCity and similar. It has the issue tracker related to code integration which you seem to want. GIT support is also there.
When it comes to the general issue tracker stuff, you have multiple options. Either you could let the boss and secretaries share backlogs with the development team, or you could create a separate backlog for them to keep other tasks in that backlog. Visual Studio Online offers multiple backlogs, sprints, kanban boards, etc...
So depending on your needs, you could separate out the boss and secretaries to their own workflow, or work out a way to include them in the developer teams.
Regarding pricing, usage for MSDN subscribers are not included in the 5 free licenses. That is, if most of your time are MSDN subsribers already, then you could add 5 people (a few bosses and secretaries) free of cost.
Disclaimer: I haven't used this tool my self, but reading your question it seems to be an interesting match. And I'm not affiliated with Visual Studio Online.