「[実家](https://eikaiwa.dmm.com/uknow/questions/965/)で[ペット](https://eikaiwa.dmm.com/uknow/questions/38643/)を飼っています」＝ We have a pet at my parents' home / My parents keep pets / We have a dog/cat at home
「実家」は「parents' home」という言い方になります。直訳すると「親の家」で、つまり、自分が生まれた育った家という事です。
「飼う」は「have」や「keep」という言い方になりますが、「have」の方がネイティブっぽくて自然です。
「ペット」は「pet(s)」という言い方になりますが、ペットの種類を言った方がいいと思います。例えば、「cat」や「dog」など。
A 'pet' is a domesticated animal which people keep at home for companionship. You can not have a pet that is kept elsewhere other than your home because it is always kept for companionship. Dogs, for example, are often referred to as 'man's best friend'. Pets are lovable. So, in your statement, you may add, 'which we all love very much' or 'which they love dearly'.
So, you may say:
My parents have a pet which we all love very much.
or
My parents have a cat which they love dearly.
pet'（[ペット](https://eikaiwa.dmm.com/uknow/questions/38643/)／愛玩動物）は人間が家で[飼う](https://eikaiwa.dmm.com/uknow/questions/44763/)伴侶としての動物をいいます。
'pet' というのは伴侶として飼われるものなので、家以外の場所で飼われているものについて 'pet' と呼ぶことはできません。
例えば、犬はよく 'man's best friend'（人間の一番の友）と呼ばれます。
'pet' は愛らしいですね。ですから、この文にも 'which we all love very much' または 'which they love dearly' というフレーズを加えることができます。
次のように言えます。
My parents have a pet which we all love very much.（両親がペットを飼っていて、みんなですごくかわいがっています）
My parents have a cat which they love dearly.（両親が猫を飼っていて、すごくかわいがっています）
If you wish to explain you have a pet in your parent's house, then you can use the above statement. As pets are invariably animals kept at home, it is probably not necessary to say 'at home' - unless it is something like an elephant, which normally would NOT be kept at home.
You can use the term 'family pet' to indicate that the pet is part of the family but stays with your parents' in their home.
-We have a family pet that stays with my parents.
family pet'（家族のペット）で、実家で飼われているもののそれが家族のペットであることを表せます。
-We have a family pet that stays with my parents.（家族で実家でペットを飼っています）
"My pet is at my family's home."
When you phrase it in this way, it specifies that you might also live there with your family.
"I have my pet at my parent's house."
A simple way of saying that you own a pet, and they are currently staying in your parents' house.
"My pet is at my family's home."（私のペットは実家にいます）
これは、話し手が家族と共にそこに住んでいる可能性もあります。
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"I have my pet at my parent's house."（私のペットは実家にいます）
ペットを飼っていてそれが今実家にいることを伝えるシンプルな言い方です。
Their' is used opposed to 'There' and 'They're, as 'Their' is used in as a possessive pronoun.
when using 'live' in this context it is describing that they stay at the parents home.
'pet' is the term given when you own an animal, normally a pet dog,cat,fish etc..
Pet: An animal that is kept at your home, you look after it by feeding it, cleaning it and giving it a place to sleep.
Parents' house: The place where your parents live.
Having a pet means you have a non-human being living with you, an animal of some kind that you feed, bathe and give a home to.
This animal is kept close to you because you need to care for it and also love it in some way.
This pet lives with your parents in their home.
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