Color scheme:

maroon: correction 

indigo: suggested improvement

A Dominating Puppet.

I have 3 small dogs at home.

They belong to the breed of Chinese Crested Dogs. ( had grammar wrong and new sentence formation is suggested)

They are hairless everywhere except the head, the tail tip and the toes. (grammar was not wrong, just sounded a li'l awkward)

The absence of hair on them is very convinient for life in a city apartment, especially, if you work on a full-time basis and you don't have enough time to fix up your home every day.
Earlier, I had only one dog and it would get lonely whenever I had a long day at work. I felt guilty for it. ( or used to feel guilty )
Then I bought the second dog... And then the third appeared :-)

Now they live together. They have a lot of fun living together. And I like watching their behavior at home as well as on a walk. It is relaxes me and sometimes it gives me a few managment lessons:)

(in English, it's grammatically wrong to start a sentence with 'and', though it's ok in a conversation)

When dogs start living in a team they usually create a hierarchy instinctively, with standart roles. One of the famous roles is a "Boss" or "Alpha male" (but sometimes it could be "Alpha female").

(don't use the article 'the' if you haven't mentioned the following word earlier. an exception is made for very famous nouns like the sun, the moon, the president etc)

In my dogs team, the smallest in size dog is their "boss", because it likes orderliness more than others. It ensures compliance with the rules and resolves conflicts. ( could also be dogs' team )

"Strong love for orderliness" is an innate quality. Although iIt is the smallest in size, but Iit does not need a lot of physical strength for retaining dominance, because it has a high level of intelligence and motivation to manage and to keep peace in its small team.
It's the same for in modern human teams:) (what you wrote was a clause, not a complete sentence)

Good job! I tried to be as helpful as possible. I couldn't but notice the use of some very nice words. It was also an interesting read and a witty management lesson))

A Dominating Poppet.

I have 3 small dogs at home. Their breed name "Chinese Crested Dog".
They are hairless with hair (or "wool"?) only on the head and on the end of tail and legs.
The absence of hair is very comfortable for life in a city apartment, especially, if you work on a full-time work and you don't have enough time for fix up your home every day.
Early I had only one dog and it was lonely if I have had long working day. I felt guilty because of it.
Then I bought the second dog... And then the third appeared:-)
Now they live as a trio. They have a lot of fun living together. And I like watching their behavior at home and on walk. This is relaxes me. And sometimes this gives me a few managment lessons:)
When dogs start to live in a team they usually instinctively create the hierarchy with standard roles. One of the famous roles is a "Boss" or "Alpha male" (but somewhere it would be "Alpha female").
In my dogs team the smallest in size dog is their "boss" because it likes orderliness more than others. It monitors compliance with the rules and resolves conflicts.
"Strong love of orderliness" is an innate quality. Although it is the smallest in size, It does not need a lot of physical strength for keeping dominance, if it has a high level of intelligence and motivation to manage and to keep peace in its small team.
As in modern human teams:)