I think I am a good man but...

[tectak]

I think I am a good man but
hands that work don't rest to pray. I'd rather go with "can't". To not do connotes having the capacity to do so, but not the will; to can't do connotes having no capacity at all. And it seems like the speaker actually wants to pray, anyway.
Hours pass in sweat and sweet,
sweet hope that every day will end;
then home to fall into the fold
of old familiar things. I think the cliche here works. I mean, it is enhanced by rhyme.

From where I sit I watch you  
as saintly sleep puts arms
round both of us;
then gently, I pick you up I think a comma before gently would make gently sound gentler. It's in the pause for breath, I think.
and wrap you in warm blankets
made from softer stuff than me. The image I get here is that the dad falls into sleep in his chair, then he somehow wakes up to wrap his son in blankets. I feel like those two should be switched. 

Your mother sits alone
in the kitchen made of mirth
and madness, songs and sadness… "in the kitchen made of mirth and madness, songs and sadness" feels like a dud. The mixture is too abstract a collection for me to strike a strong image.
while we, just you and I,
climb up the stairs. Is the narrative in this stanza a direct continuation of the earlier? If so, I think it should be somewhat clearer -- I thought earlier that the dad was already looking at his son while the babe was in his crib upstairs. Maybe rearrange the two stanzas, and use the space in vaguely describing the kitchen to concretely describe the opening scene?
This is how each day should end. 

You will say your prayers
when you are old enough
to speak the unknown words. "the unknown words" doesn't give me anything clear. What exactly do you mean by "unknown words"?
I once did, too, when just like you,
I heard my father whisper
in the hiss and drone of night. I sort of don't get this stanza. I never heard the speaker whisper words in front of his babe here (I mean, at this point, he says, he can't pray anymore, and never once is it mentioned that the speaker speaks otherwise. Everything so far has been silent.).

I know now that he cried;
for all his love was in his words
and all his words were in my dreams. And as I did not get the earlier, so do I not get this.
That is why, my baby boy,
all my dreams are wrapped
inside a blanket, softer than me.  But I do get this. Sweet.

I think I am a good man 
but I have no time for prayer. Alright.

Soft sounds for a soft moment. Either that, or I'm getting sleepy (or, er, lovesick?) Thanks for the great read!

Fine crit, river.Thank you. There are holes to fall in to which the writer digs for himself then walks on. You found them for me and filled them in. I will wrestle with this one.
I listened to a father talking about his life on TV recently (UK election interview). He was a hard working guy who came home tired to a tired wife but because his hours awake and at home were limited he opted to take over childcare(big issue) each evening to give his wife a break.
He talked about the good times and bad times around the kitchen table and how the "gift" (sic) of a son had changed his relationship with his life, his wife and himself. Throughout the monologue he avoided any references to god-grat but by his very words he was praying.
Your observation on the cannot/ do not choice is one that I pondered. He gave the impression that he had no wish to pray but could if he chose. He chose not to and that is reflected in the dual meaning of the last line...along with the pointed use of the "but" word.
The rest is up for grabs. Thanks again.
Oh, the unknown words? Prayers.
Best,
tectak