When I attach something sensitive like a analog camera and LCD screen to a car battery along with a switched high amp load like a power door lock actuator, I get video problems when the load is switched on AND switched off. Why is it that in a car, there is no problems with those same devices in the same scenario? What do they use to isolate these high amp devices from interfering with other electronics?
This is a bit vague, for example "a car" - which car? Where are you getting the power from in the car? cigar lighter socket? the battery terminals? Also, exactly how are you connecting the actuator/LCD/camera to the standalone battery?
Essentially, the answer is that they use regulation and filtering in the circuits, so for example a sensitive module like your LCD screen would have a local power filtering circuit, which would consist of something like:
If you can tell us a bit more about your malfunctioning circuit then specific advice can be given on how to correct it.
Okay, from the comments and data it looks like the transient and power sag are causing issues with your camera module. It appears the camera module does not have a regulator onboard.
It can be quite hard to design a switching regulator if you have had no experience with them previously, so a ready made module looks like the best way to go. There are many modules on eBay that will do the job, such as this one:
The above module can handle an input from 3.5-28V, and convert to an (adjustable) output between 1.25-26V. There are more options on this page (I would avoid the really cheap modules)
Okay, we have (finally) discovered that you are using a single CAT5 cable for all the wiring. Sharing the 4A actuator power with the camera/LCD modules wiring this alongside the sensitive video signals is undoubtedly your problem. CAT5 is not designed to handle power like this, you absolutely need separate cabling for your actuator.
Take a look at the table of specs from the Wkipedia page, particularly note the resistance per meter and the maximum current rating: