Heartbroken owner, Keri Arbel, believes the dogs were stolen to order from the family's smallholding near Gobowen on Thursday night.
The three dogs, all rescue animals, slept overnight in a caravan next to the family home.
One, called Emily Rose, was heavily pregnant. She was stolen, with two other dachshunds, Greta and Nancy, at about 11.30pm.
Keri said: "We were in the house when we heard the most awful screams, I have never heard anything like it before - it must have been the girls being taken. We rushed outside, went to the caravan and they had gone. We couldn't believe it.
"Some lads that were working on the A5 roundabout came across and said they had seen a white van disappearing. We have told the police what they told us."
Two of the dogs, Greta and Emily Rose, were rescued from Serbia by Keri.
"When we got Emily Rose we realised she was pregnant," she said.
"I didn't want them living in kennels so they are with us on the farm throughout the day and I bought them the caravan to sleep in at night."
Another dog, Duchess, rescued from a South Wales puppy farm, was in the house that night and was not taken.
Keri is appealing to people to contact her or West Mercia police if they have any information about the missing dogs or see dachshunds offered for sale.
"Someone must have know we had the dogs and where we kept them," she said.
"I will never forget the screams they made and I will continue looking for my girls until we find them."
She said appeals on social media had been shared across the country and in Ireland.
North Wales Police Rural Crime Team recently issued a warning on Facebook about the theft of dogs not only in Wales but across the English borders.
Officers said: “Criminals are targeting valuable dogs for selling on as there has been a market for them during lockdown. Be aware.”
Anyone with information related to the incident in Gobowen should call Keri on 07854 146625 or call West Mercia Police on 101 quoting the crime number 10I31072020.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org