A Canadian mother and her seven-year-old daughter, who has autism, have been detained by US Immigration and Customs Enforcement (ICE) in Texas since Saturday, family members have said.

Relatives of Tania Warner and her daughter Ayla Lucas say they were detained unlawfully. They are uncertain about what problem ICE found with their immigration paperwork.

Tania Warner and her daughter are both Canadians, with Warner originally from British Columbia. The Canadian broadcaster CTV News reported that they are being held at the notorious Rio Grande Valley Central processing centre in McAllen, Texas.

Warner, who is said to have moved to the US five years ago, lives in Kingsville, Texas, with her husband, Edward Warner, a US citizen.

The family was driving home from a baby shower in Raymondville, Texas, on 14 March when they were asked at a border patrol checkpoint in Sarita to provide documents, according to Edward Warner.

He presented his identification, Tania presented her Texas driving licence, her work visa and her “actual visa”, he told CTV.

“After that, they took her in, saying that they needed to fingerprint her to get more information, and she never came back out,” he said.

ICE agents later came out and took Ayla in for fingerprinting, he said. She also did not return.

Amber Sinclair, who is Tania’s cousin, told the Guardian that Tania paid for processing help for her documents to ensure everything had been done correctly.

“She has a social security card. She has a functional visa. That’s good until 2030, so I don’t understand why they’re stopping her and detaining her,” she said.

Sinclair, who lives in Houston and is a dual Canadian-US citizen, says there have been many ICE checkpoints set up in Kingsville as it is about 120 miles from the border with Mexico.

She fears Tania and her daughter could be deported and end up separated from Edward and the rest of the family, along with her job.

The family is scrambling to raise enough money to pay for legal help, she said.

Documents Edward Warner gave to CTV indicate that his wife is categorised as a “Lawful Alien Allowed to Work”. He described it as “scary and really frustrating” that the pair have been detained when “they have paperwork that’s good”.

At Rio Grande Valley Central, Warner said he has learned from phone calls with relatives that mother and daughter are being held in poor conditions.

“She’s having to use the mat from the floor to get a proper cover to keep warm. The food is terrible … it’s overcrowded, very loud, and they’re just very stressed out right now,” he told CTV.

Global Affairs Canada, the federal ministry that handles consular services and diplomatic relations, said it was “aware of multiple cases of Canadians currently or previously in immigration-related detention in the US”.

“Consular officials advocate for Canadian citizens abroad and raise concerns about justified and serious complaints of ill-treatment or discrimination with the local authorities but cannot exempt Canadians from local legal processes,” a spokesperson said. “Due to privacy considerations, no further information can be disclosed.”

Edward Warner told CTV that the Canadian consulate in Texas told him it could only help if Tania and Ayla were looking to return to Canada. Edward has launched a GoFundMe to hire a lawyer.

Audrey Macklin, an immigration and refugee law professor at the University of Toronto, said that detention of children in particular, even for a short period of time, can be traumatic and have severe, enduring consequences.

She said that while Canada has limited power in this scenario, its representatives should be requesting to visit the family in detention and provide legal counsel.

“It raises concerns for Canada … about its own obligations toward its nationals,” she said.

It is particularly those working and living in the US, who rely on documentation, who are at risk of being detained, she added.

“This really just illustrates the cruelty of the US system. Basically, people are being kidnapped and thrown into detention in abusive, inhumane, unsafe conditions.”