Greyhound and the cats *sigh

Question
I just got a 9  year old  greyhound  ~never  raced~ old owner  was military.  
They  started off in Australia then on to  Hawaii,  California made it up  here
to ND and  then he got sent back to CAL.

So I had  had a  greyhound  before.. obviously  different personalities here...

My  house hold:
Dalmatian lab  mix about  11 with  bad  hips
4  cats (bold  to  one  needing happy pills)
1 Dove in a  cage,   a  1  year old  toddler and  11 year old  boy.
New Greyhound 9 years old non  racer.

Problem:  The  greyhound  has never seen cats~ I am assuming~  I  tried the
leash trick,  went  back to that after  1  day of  access,  cats wait until this  dog  
sleeps. I  did the  gates,  meet  and  greet  ... cats  were wary  and  still slunk  
around the  dog chases them.
I was holding  1 cat in the  other room, back turned to the dog not realizing
this  dog  snuck  up on  us and she grabbed and lightly bit the cats leg. NOT  
NIP.
I am rethinking  everything and maybe she  wanted to taste a cat to see if its
good.
Would a  muzzle do for a  few weeks? I wouldn't really like that idea.
We  were all  so use to sleeping together  cats, dogs  people  and  this is a
new one for us.  I am use to bringing in a  new  animal  but this one...

Give me  more  suggestions... I will try anything.

P.S. Greyhounds are not  wild like people  say they are.. they are fine around
small children. They  just  like to run. Big skinny lump of  fur.


Answer
While many dogs are not like their descriptions, my book does say Greyhounds are implacable enemies of cats.  Bringing one into a household with cats may not be a good idea.  About all you may be able to do is keep them separated.  Crating the dog may be a good idea when you aren't around.  

It is only natural that a puppy resists its crate at first. What the puppy wants more than anything else is to be others, you, anyone else in the household, and any other pets. In our modern society, even if we are home, other things distract us from the attention an uncrated puppy must have. The only real solution is to crate the dog when you aren't around. The dog may be happier in its den than loose in the house. It relaxes, it feels safe in its den. It rests, the body slows down reducing the need for water and relieving its self. Dogs that have been crated all along do very well. Many of them will rest in their crates even when the door is open. I think the plastic ones give the dog more of a safe, enclosed den feeling. Metal ones can be put in a corner or covered with something the dog can't pull in and chew. Select a crate just big enough for the full grown dog to stretch out in.

Leave it some toys. Perhaps a Kong filled with peanut butter. Don't leave anything in the crate the dog might chew up. It will do fine without even any bedding. You will come home to a safe dog and a house you can enjoy.

A dog that has not been crated since it was little, may take some work. Start out just putting its toys and treats in the crate. Praise it for going in. Feed it in the crate. This is also an easy way to maintain order at feeding time for more than one dog.

The "shut the puppy in a safe room" is a fallacy. Very few houses even have a safe room. How many of us have a room with a hard surfaced floor and nothing else? Most rooms have electrical cords to chew if nothing else. In addition to destroying anything a bored puppy finds to chew, it may choke or have intestinal blockage from the pieces. I had a friend that left her dog in a "safe" room. It ate a hole in the floor covering. The safe rooms fail to give the dog the comfort of the enclosed space their instinct requires. Nor do they restrict activity extending the time the dog can go without relieving itself.