I work remotely so my dog thinks that I amhave the whole day available for him when he gets bored.

WeMy husband and I were wconsidering with my husband about buying second dog to provide our older dog a new friend.

Wondering doesn't fit well in this usage.
Husband is included in the we so it is not needed but by making the subject "My husband and I" we can fix it.

One day, we decided to watchvisit puppies inat the breeding nearbynear by breeder.

It would be more concise to say you were visiting the puppies not watching them.

We spent about 2 hours playing with the puppies and talking with the owners.

It might seem not necessary but saying "the owners" is more natural.

Finally, we came back with a new puppy this evening and Bazyl was so surprised!

It would be "a new puppy" or "the new puppy".

Now they are near me playing together near me and I feel that it was a great move in our livfe.

Live is a verb, you mean to say "life".
The first half of this sentence may actually be correct but it does not flow well to me.

I work remotely so my dog thinks that I am whole day'm available for him all day when he gets bored.

We were wondering with my husband about buying second dog to provideMy husband and I were thinking about getting (or adopting) a second dog as a new friend (or companion) for our older dog a new friend.

One day we decided to watchlook at puppies in the breeding (?) nearby.

I'm not sure what is meant by the word "breeding" here. Could it be a pet store or animal adoption center?

Now they are playing together near me and I feel that it was a great move in our livedecision.

I work remotely, so my dog thinks that I am whole day availablI'm there for him whenever he gets bored.

We were wondering withtalking to my husband about buying a second dog to providgive our older dog a new friend.

"Wondering" implies that you thought about it to yourself, but if you consulted with your husband then it makes more sense that you talked to him about it. "Provide" is correct, but "give" in this context sounds more natural and is what would probably be used in spoken English.

One day we decided to watchlook at puppies in the breeding nearbyfrom a nearby breeder.

"Look at" implies that you're going to see puppies with the intention of buying/adopting one, whereas "watch" seems like you are just watching them for fun.

We spent about 2 hours playing with the puppies and talking with the owners.

Finally we came back with a new puppy this evening, and Bazyl was so suprised!

Now they are playing together near me and I feel that it was a great move in our livedecision.