Charging SLA Battery
It is extremely common to connect a battery charger, a SLA battery, and a load in parallel - millions of cars are wired that way.

If the charging source can supply more current than the load needs, the excess goes to charge the battery.

If the charging source can't supply enough current to supply the load, the battery will discharge to make up the difference.

The battery will switch between charging and discharging automagically as the load or charging source change - no need for any external control.