I looked at an LM338 / LM817(?) but I wasn't confident in understanding the typical application circuit in the data sheet. That would be my first question: Is the LM388 suitable for a 2A limiter and how would one set it up. My input voltage will be more-or-less fixed, either 0V or 14.4V.
The dropout voltage of the 317/350/338 and most other integrated regulators will be way too high for this application plus their reference voltage is in series with their dropout voltage.
There might be some lithium battery charge controllers suitable for this application.
So my second question. Is there a way to allow current to flow from either the utility socket or the battery to the dash cam, but to limit the current from the utility socket to the battery only. Some form of op amp buffer or something?
If the dash camera is directly connected to the SLA battery, then placing the current sense in series with the SLA battery instead of in series with the input will allow the current regulator to ignore the current drawn by the dash camera. Then the regulator will power the dash camera but apply a controlled charge to the battery. However if the current drawn by the dash camera is small compared to the maximum charge current which is likely, then it can be ignored.
Note that the charging voltage requirements for a SLA battery are different than for a flooded cell starter battery. The maximum charging voltage is lower which is actually a good thing because it allows some leeway in the dropout voltage of the regulator.
A low voltage disconnect should still be used with the SLA battery because they are also damaged by excessive discharge.
The simplest possible design and probably what I would go with is a simple low dropout external PNP voltage regulator using beta current limiting which requires no sense resistor like the
Linear Technology LT1123. The circuit would need to be modified to handle the input voltage being disconnected, maybe by adding a germanium or schottky power diode in series with the input. That still leaves including a low voltage disconnect though.