Start with the following link:
https://www.howtogeek.com/66214/how-to-forward-ports-on-your-router/
Then use your router's manual, the camera manual, and your laptop to plan out the IP connectivity/IP addresses you wish to or need to use.
Use the device and IP addresses diagram shown in the tutorial as a model.
And the next two links may help with some specifics....
https://portforward.com/
https://portforward.com/router.htm
Because you will be traveling and most likely working in different environments you will need to know how to and be able to reconfigure your devices (laptop/router/camera as circumstances warrant.
As for a specific router, I like the Linksys WRT1900AC. However, there may be some other router more suited for "road warrior" travels.
Work at home to get the camera working albeit a DHCP IP address or a Static IP address. A static IP address should be viable and would be a constant that you would always know. Just reserve the camera's static on the router remembering that that static IP must be outside of the DHCP IP address range set up on the router. Plus the static IP address should be reserved on the router via the camera's MAC.
See what you can do. Sketch out a diagram, list the steps that you need to take, and then set it up. Then, if there is a specific problem, then that problem can be focused on. And you will know much more about the devices and their configuration. Makes it easier to troubleshoot.
Also: you may end up determining that the camera is indeed faulty in some manner. Nothing you do may work.