I am sorry to hear you are worried about Rex. My name is Rebecca. I am a veterinarian and will do my best to help.
Is he eating, and drinking? Any vomiting at all?
I am concerned he ate something that is causing these symptoms. I am glad to hear he has pink gums, and is no longer straining to defecate, and the foaming is decreased. The shaking and being unsteady are concerns. If he is eating and drinking, that is a good sign.
If this happened to my own dog, I would be doing a good exam: Take his temperature with a rectal thermometer (normal is between 101 and 102), feel his lymph nodes and palpate his internal organs, listen to his heart and lungs, feel the quality of his pulses, test reflexes, look into his eyes. In addition, I might do some basic blood tests, to check for things I can't learn by physical examination: blood sugar, electrolytes, etc.
So the best thing would be an exam by a vet, going to an emergency clinic. However, if you think some of his symptoms are getting better, you could try keeping him stable by keeping him hydrated by offering water, broth, and Pedialyte if he is not eating, monitor his gums to be sure they stay pink, taking his temperature if you can, and watching him until you can get him checked out by his regular vet in the morning.
This does not sound like what we see with rat poison or antifreeze, but there are many other things he could have gotten. Strychnine is not used much these days to kill rats, but it can cause seizures, shaking, tremors.
Let me know how he is doing and what else I can help with or answer.