A Cat, a bat, a rat.

[Kerbonzo_beenz]

All from the same family,
siblings by blood; the cat, the bat, the rat
The cat sleeps on their chairs,
eats the food the people share
With a nasty ear and a threatening snare, 
she wouldn't make it past May in this cold air

I suppose the bat would sleep on chairs too
but certainly wouldn't eat the people's food--
Too scared
They come around, she flits away, agenda and all  Reword this slightly, the rhyme is a bit of a stretch
right over to the next side of the people's wall 

The rat, a blood-sucking, badly-behaved rabid animal
terrorized the poor cat
The rat originates from the other side of the wall
But she has no true home    The fact that the rat is homeless doesn't read repeating
With light eyes and an expired relationship with the bat,
The rat roams about
in search of home, not just a house
She has no purpose,
no one will love her. Strong ending

-VikaJigulina

I like the metaphor between these animals, very relatable to humans.
Feel like this may be a bit personal to your own life, not sure.

When you say "those people" is it meant to show that
the cat, bat, and rat are in a adoptive relationship?
If so, maybe try and find a better way that's less
vague to explain that. 
Do whatever feels good in the gut though.

This was very clear and precisely worded,
can understand your overall goal for the poem.
Good work!