ya. you need the fluidity of the original, i think. and no more punctuation than necessary.
i took it and played with it a little (fullknowing susan will probably snap at me)
first though, it seems to me with the first line, the only reason it doesn't start with an "It's" is because that would make 11 syllables. i wonder if that could be worked around, but for now, it stands as is.
i think the beginning is otherwise solid, somewhere in the middle part lines start to droop over into the following lines, especially the 8th line ending on 'with'. i took myself some devilish freedoms there. i love the lines
"They shy away from sleep when I'm around
Self-flattery it is to think them mine."
i think the end has a good punchline, with the cats intention, having the bed for themselves, but its a little awkward in how its presented.
one thing i think is a fun addition in a sonnet is to sometimes jump in an image, rather than using only 'and's, you can throw in a comma. the beginning for instance: "It's easier to submit, pet the cat". commas can also be used to emphasize some curious internal rhymes.
anyhow. the rest of my critique you'll find in my edit of the poem. discard or find something useful. i do think you have a natural voice, for whatever poetic forms, and thats really what matters.
k
Easier to submit and pet the cat:
In so doing, his eyes no longer haunt
Except that he is never satisfied
Though I stay awake with him at night.
He brings along his brother, more the same.
The two of them, paw and tug and whine
In the bed that seems to small for all.
If I could dream, I would take them gladly
Along the rocky outskirts of my mind.
They shy away from sleep when I'm around:
Self-flattery, it is to think them mine
When all along they've had a simple plan
To see me fly away, and leave behind
This here bed, for themselves, more room to stretch.