There are two bits of trickyness.
Wiring two in parallel will equalize them provided no diodes are involved. An easily measurable difference will result in a large current circulating until they have equalised, which SLAs do not like. They are two sets of plates very close together. With too much current heat is generated, but is not evenly distributed and so warps the plates. in itself this is not good, if the warping gets too far, the plates contact thus shorting the cell. The result of that can be very messy, what with spraying the surroundings with sulphuric acid.
Wiring two in series is not a problem. Using a centre tap to provide an intermediate voltage can lead to problems. The 0-12 volt battery carries both loads, the 12-24 volt one just the one load, so the 0-12 volt one discharges deeper in a given length of time. If they are both charged together, you get to where one, having a deeper discharge, requires a larger charge and doesn't get it, the other gets overcharged.
Best to disconnect them and charge separately. The charger is probably designed for a single battery anyway. The inverter option does make life a lot simpler.