I've run into problems with realtek gigE nics on Linux, FreeBSD, and Windows. I'm convinced their hardware/firmware has a timing issue where if the wrong things happen, the descriptor indexes get unsyncronized. This can lead to network stalls, but also wild writes. IIRC, reset behavior is weird too; vague because it's been a while since I looked, but I think if you get a network stall and do a reset, the card may receive and DMA a packet into RAM in the process ... something like that anyway.

I have systems where the FreeBSD base driver consistently stalls, but the realtek provided driver works mostly ok; but the realtek driver is full of undocumented flag setting, so who knows what it's doing... it also sets the NIC to emit pause frames when it runs out of RX buffers which I never want; things will be much better if packets are dropped when RX buffers are full.

I would love to have the equipment and time to figure out what's going on, but a) realtek probably should be the ones to do it, b) switching drivers usually works at no cost, and swapping to intel almost always works but you need slots and cards (ebay gets you multiport 1g for $10, 10g for $20-$30 though). I've heard realtek is good at 2.5g and intel isn't; but I haven't run enough realtek 2.5g to know.

One suggestion though: rather than doing this all on a single LAN network and having to deal with adding exceptions for devices that still need access to the Internet during 'bedtime' periods, I suggest creating a separate VLAN for devices that need 'bedtime' enforcement and put those devices there, while leaving your 'always online' devices in your main VLAN where access to the Internet is always available. This way all you have to do is simply change your firewall rules for that VLAN to enforce bedtime, which removes the extra rules needed for exceptions.