Lead Acid Battery Charger with Load in Parallel
Just connect your load directly to the battery.  The charger will provide 350 mA when the battery voltage is low enough.

Battery current = charger current - load current

Yes, it's really that simple.  If the load is drawing 50 mA and the charger is putting out 350 mA, then the battery will be charged with 250 mA.  If the load draws 350 mA, then the battery current will be zero.  If the load draws 1 A, then the battery current will be -650 mA, meaning it will put out that much current.

The battery will be drained some whenever the device draws 2 A, but will then be recharged over a longer time by the charger when the device only draws 50 mA.  You need to make sure of two things for this to work:

The maximum high-current drain times the maximum time it needs to be sustained is well within the battery's capability.  This guarantees that the battery can still deliver power at the end of a long high-current discharge event.

The average load current is less than the average charge current capability.  This guarantees that in the long run the battery will be charged.



Both these seem to be true from the limited description you ahve provided.