with site to site vpn's you "should" be using the same hardware all the way through. the fact that "work" has provided you with a router means they should be able to setup the site to site link. rather than dd-wrt go for a draytek 2830. the gui is simple and site to site vpn is well documented and easy to setup.
not to mention it is also gigabit all the way through support dsl and the 2860 supports VDSL (which i use at home)
sorry but looking at the diagram again, looks like you are double natting the traffic through your router which is really bad.
i have setup site to site VPN's and this is bad practice. Setup the cisco as the the main router and for internet access. once internet access has been confirmed setup the site to site vpn. you may need to add a static route to say all internet traffic go through the DSL/WAN port. Data that needs to go over the VPN will already know how to router but you may have issues with DNS
Get your IT to setup in. if they know anything about what they have provided then they should be able to help.
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