Since you are merging two nets, you should use TAP interfaces.
TAP (as in network tap) simulates a link layer device and it operates with layer 2 packets such as Ethernet frames. TUN (as in network TUNnel) simulates a network layer device and it operates with layer 3 packets such as IP packets. TAP is used to create a network bridge, while TUN is used with routing.
This way, you will be joining the HQ network with the branch network like if you plug a (secure, pre-shared key may be ok) ethernet cable between them.
But this will likely crash both environments if they are operating now without knowing one about each other. Maybe the HQ router has the same IP as the branch one, or maybe not, but they are both acting as DHCP servers and now they will be on the same network.
Do you really need to merge both nets? I think you should consider to do some network design and let the HQ on the 192.168.0.0/24 but change the n-th branch to 192.168.n.0/24. Then you can do a TUN OpenVPN setup and route between branches and HQ in a hierachical way. It will save you some bandwith too by not spreading irrelevant broadcast traffic over the tunnel.