Dachshunds Purdy and Pippin were taken from their garden in Thirsk, North Yorkshire, on 23 January 2021.
Ruth Benson said she and her children had been left “heartbroken” since the disappearance of the “priceless” pair.
A pet detective agency told the BBC thefts were on the rise due to a rising demand for pets during lockdown.
Mrs Benson said “Purdy is [my daughter] Ruby’s best friend, she means everything to her.
“They are a part of the family, they are not just pets. It’s heartbreaking to just not know where they are.
“Every morning the children ask, ‘Is Purdy going to come home today?'”
She added: “They are priceless to us, no amount of money will ever cover what they are worth to us.
“But, if people see [the reward] and it gets people talking, anything is worth a try to get them home.”
Please call 07857145746
Or Police on 101
Pippin on Doglost: https://doglost.co.uk/dog-blog.php?dogId=164104
Purdey on Doglost: https://doglost.co.uk/dog-blog.php?dogId=164103
Newspaper article: https://www.bbc.co.uk/news/uk-england-york-north-yorkshire-56008870