The MiFi wont have to do anything special in this scenario. All it will do is connect to another networking device.
Let your Jetpack connect to your AP that is acting like the wireless bridge by typing the WiFi password into the AP. The bridge device will have to reconfigure itself to use the Default Gateway and subnet of the Jetpack so that the Jetpack will act as the "modem". This can be done automatically with preconfigured router modes if they are available on the bridge. Otherwise you can manually configure a bridge or repeater out of just about any kind of normal AP/home router too.
Jetpacks have an admin website that you can sign into from a connected PC. Type the default gateway of the Jetpack into a web browser and sign into the admin site with the admin password for access to these features. Certain Jetpacks have limitations on the subnets that they support so I'd suggests sticking to the usual 192.168.x.x with a 255.255.255.0 subnet mask.
I'm looking to have the public IP bound to my Router for a IPSEC VPN configured on a fail over scenario. The scenario describe will assign a non internet routable 192.168.x.x to my router.
Are you're using LTE Internet (Installed), formerly Home Fusion? Bridge mode is not a supported option. You can use the DMZ to simulate it, but that uses a private IP address.
If it was me, I'd buy one of these:
Just to see if it can be used in place of the Home Fusion HBR and allow the use of any third party router. If not, I'd return it to any Walmart for a full refund.