Are the front wheels on both sides on one anti-skid system and the rear wheels on both sides on a second one?
The following is for information only.
No, the anti-skid system controls all eight brakes equally. Also, the parking brake applies to all eight brakes.
A bogie "pitch trim" system tilts the bogie at takeoff and for landing to provide additional tail clearance. The tilt mechanism levels the bogies for retraction, and the shock strut is "shortened" by another mechanism so the gear fits into the gear bay on retraction.
Touchdown is always on the rear bogies first; the tilt system "lowers", (sometimes drops!...) the forward bogies as aircraft de-rotation occurs. That's the small secondary bump one feels in an A330/A340, (some have mistaken this for the centre landing gear touchdown, but the A330 doesn't have this gear and I can assure anyone that it still "bumps"...).
The wheels are numbered, 1,2 - 3,4 across the front bogies, and 5,6 - 7,8 across the rear bogies.
Not sure what would cause just the rear bogies to lock and remain locked but the scenario (all four evenly destroyed), fits a "signal-to-a-system" vice any mechanical/physical impediment (frozen, etc), that prevented all four from rotating.
I believe if the park brake is set to "ON" prior touchdown, park-brake pressure would be applied to the main gear at touchdown. Placing the Park Brake selector to ON isolates the main and alternate braking systems and provides Blue system pressure @ ~2500psi.
The AOM states:
CAUTION
As long as the handle is not in the «ON» position, the parking brake is not applied.
If the park brake is selected ON in flight phases 6 & 7, (above 1500, to touchdown), an amber ECAM warning, PARK BRAKE ON, is presented, associated with a single chime.
There is some discussion on PPRuNe on this exact question, but is inconclusive. But the statement above seems pretty clear - if the handle is OFF, then the brakes aren't SET - otherwise, they're ON, period.