So, I would go into device manager, open any listed mouse devices, go to the advanced power options tab and disable "allow this device to wake the computer".
Any minute vibration in the room where there is a mouse that is able to wake the computer will cause it to wake unless you disable that option. Often, you have to also open and do the same thing for all listed keyboard options EXCEPT the one actual keyboard. Sometimes mice are listed in there under keyboards because they can be used as an on screen keyboard device in some cases.
Disable any keyboard option for "allow this device to wake the computer" that is not the ACTUAL keyboard, and that might take a couple of trial and error steps to do, and also the actual mouse itself. Then, when you need to wake the computer, simply press any key on your keyboard. Much harder for the keyboard to accidentally wake the computer than the mouse.
And, I'm not saying that IS the problem, but eliminate that as a potential issue first, then seek out other potentially problematic sources later. It is very unlikely that "Realtek GBE family controller" itself, is the problem. Thousands of people using those network adapters and not having the same problem you are, with the same configuration. I agree, the family gbe controllers leave much to be desired, but we can't blame EVERYTHING on them, even though they kind of suck.