If you expect to segregate the data coming over the fiber link into two VLANs - one for camera use and another for the devices connected on the WiFI AP, then you'll definitely need a switch that supports VLANs (usually some sort of managed switch) at the driveway gate (I didn't research to know if the current switch has that capability or not). Once the switch tags the different traffic with the applicable VLAN number, traffic it will be segregated, but sent over the same fiber bridge to the main house.
That being said, since these cameras are going to have to use VLANs and not be on a completely separate network, there is really no reason to add the second network card in the BI machine. People typically add a second card when they can put all of their cameras on a separate network (physically) and one port goes to that camera network and the other port goes to the regular home network. You'll effectively accomplish the same thing over VLANs, but the requirement to have two network cards in the BI doesn't exist when you use VLANs. Therefore I would remove the nic/direct connection to the router and just hook the BI machine up to the switch.
So, you'll need to create a VLAN for camera use only, and at least one more VLAN for all the other traffic on your network. You'll need to set the VLANs up in your router/firewall device as well as the individual switches. (This assumes your firewall/router is going to handle all of the routing tasks on the network. If you are going to set up the switches to act as a true layer 3 devices, you set everything up in the switches and you won't even have a separate router/firewall. This is NOT what most people do unless they are trained IT professionals and deal with layer 3 switches regularly).
I would also connect the switches directly to each other and not solely through the router. Any traffic between VLANs is going to have to pass through the router, but all traffic passing on the same VLAN could be handled at the switch level. But if you have only connected the switches to the router and not to each other, you are forcing all of the traffic to go through the router which could potentially create a bottleneck. I don't think these TP-lInk switches can "stack" but higher end enterprise switches can generally be linked together via "stacking". This creates just a single user interface vs three different ones (so example if all of your switches had 24 ports, you would have a single 72 port switch with regard to the GUI/management interface. These stacking ports area also generally rated for higher data transfers. 10gb or higher stacking ports are very common and the ports are SFP+ a lot of times which means you wouldn't even need a fiber converter because you could use SFP+ fiber connectors to directly link the switches together - including the gate and hose. Now as I type this, I realize you probably need a fairly small switch at the gate location, but there are a lot of smaller 4, 6,and 8 port managed switches that have one or two 10gb SFP+ ports on them to link to other devices/switches. Now even if you can't stack your switches together (which is completely just for management purposes), you might consider switches with a couple 10gb SFP+ ports so that you can connect the switches together to help prevent any bottlenecks. Even better would be if your router supported a faster LAN port (2.5gb or 10gb, etc) so that you could use a fast connection between the router and the switches.
Hopefully that's not too much information thrown at you. You can skip all of the SFP+ information if you want, I just thought it might be something to consider because you wouldn't need the fiber converters if your switches already supported a fiber connection via a SFP+ port.
