Battery Charging

Sounds like you have something wired incorrectly....can you supply a diagram?

Never mind.

Sounds like it was installed by a sawn wit, a pair of half-wits.

Get rid of the offending 24 V charger, and put in a system with the appropriate voltage, very simple.

Any evidence the mains charger system ever worked?

You may have two incompatible control systems here.

The solar charger may not have to bother about input overvoltage or over current - because the panels have their inherent limits. If there is a fixed transformer ratio, input to output, it may have no need of output current limit. It may have a microcontroller which operates a routine - < increase output current a bit - if output power rises, increase current again but if it falls then drop current back a bit > - in order to find peak power. Measuring Amps + volts and calculating power will take a definite time. From the AC charger's viewpoint this is a load which always wants to find its overcurrent limit and sit on it.

The AC charger wants to keep fixed voltage, but must protect against overcurrent. If current limit is exceeded it may well have a "foldback" Volts/current feature that gives a fraction of rated current at zero volts and current which increases linearly with output voltage - up to nearly normal voltage. This is an unstable slope - it will bootstrap an electronic load full of capacitors from zero volts up to normal or collapse volts in overcurrent! It might shut off after a time with low output volts & overcurrent but re-start after a time interval for cooling. The solar controller may see a very low input voltage as "darkness" and shut off - it does not have to wake and check volts again very often.

So your low AC charger output volts may be because it is cycling on/off quickly giving a low average reading on a DC voltmeter - and the output to the battery may be low because the solar control thinks it is "dark" most of the time.

An oscilloscope could reveal what is happening.

Also, since many multimeters have a DC blocking capacitor on AC voltage ranges, measuring AC charger DC volts on AC range may detect an unusual "sawtooth" AC component. A fluctuating reading on DC may be a symptom but most DVMs measure over a time equivalent to several mains cycles (to avoid mains ripple causing fluctuating readings) so may not notice fast sawtooths.