People trying to get Covid-19 tests have spoken of their frustration over the length of time to book, distance to travel and delays after they arrive.
One testing site in Abercynon, south Wales, reportedly ran out of kits.
Many families had travelled there from England while some Welsh residents had been offered tests in England.
The Welsh Government said there were ongoing test issues at a UK-wide level, while contractors Serco said the Abercynon backlog had been cleared.
An official at the site told BBC Wales it had closed for a few hours while they fetched more tests from Swansea.
Nina Abel, from near Chippenham in Wiltshire, had a 90-minute drive with her children, aged five and two, to Abercynon in Rhondda Cynon Taf for a booked appointment at 09:30 BST on Tuesday.
"I spent all day yesterday refreshing the government website every 15 minutes to try to get appointments for my five-year-old, who's been in school over the last week," she said.
Dr Abel, a GP, is meant to be in work on Wednesday, but could not get a prioritised test through her local clinical commissioning group.
She was told to wait until 12:30 BST for the test in Abercynon because of delays after being informed there were no tests available at her appointed time.
"It's a deeply frustrating situation," she said.
On keeping her children fed and entertained in a car park, she added: "I've only got snacks but we've got Frozen 2."
Other people who travelled to Abercynon, in the south Wales valleys, had similar tales to tell.
Hannah Summers, from Bristol, drove earlier on Tuesday for an hour and 20 minutes for an appointment at 09:30 BST.
"We finally managed to get an appointment yesterday," she said.
"My daughter, who is five, has a heavy cold and it's turned into classic Covid symptoms.
"I tried from 3pm. We were offered Bristol but [the system] timed out and crashed," she said.
"This was our closest option. I work in early years and I'm a childminder so I've had to cancel everything."
Her daughter Maia is with her for a test while her twin has stayed at home with their father.
Ms Summers said: "The novelty is wearing off. I'm not sure I've got enough food.
"It's put all of us on hold. I can't go back to work until I get a negative result."
She said she had been told her QR code would still be valid for a test "around midday" despite it being for an 09:30 slot.
Ms Summers described the situation as "chaotic", adding: "The online site is still showing Abercynon as having availability. So another load of people will have turned up."
I’m told people have turned up for their test appointments today at Abercynon and been told they’ve run out of tests and “hope” to have a delivery at 1230. It feels like chaos. @MattHancock can you sort it?— Chris Bryant (@RhonddaBryant) September 15, 2020
Kelwicki and Justina Milosh from Wellington near Taunton, Somerset, had come with their three children aged nine, seven and five on the two-hour journey for tests after their seven-year-old developed a cough.
The couple both work in manufacturing and do not know if they will get paid while they get the tests done.
"We just had to find a toilet in Abercynon," Mr Milosh said.
"We've got water and snacks, but obviously if we have to wait until 12:15 we need something else. It took ages to book this - five hours at least.
"I was told yesterday people had come from London."
"Plenty of kids getting a cold or a little cough. They normally get colds in September when they go back to school.
"What if next week one of my other kids get a cough?"
While families from England spoke of delays and long journeys to Wales, a Welsh couple said it was "ridiculous" that they were offered tests in England.
Lynette and Adrian Jones, from Neath, condemned the system as a "shambles" after they were asked to go to Warminster, in Wiltshire, 100 miles away.
They said they were unable to get a test in closer centres to their home such as Margam or Swansea's Liberty Stadium.
Rhondda Cynon Taff council leader Andrew Morgan said he was aware of reports of people "struggling to book a test in a local testing centre" in the area, which has been struggling to avoid a local lockdown over case numbers.
"It is absolutely vital that capacity is increased to further develop our understanding of the prevalence of the virus in communities and identify any clusters that may exist to inform the test and trace operation," he said.
Meanwhile in north Wales, Julia Massey from Abergele in Conwy said she had to "fight" to get a Covid-19 test for her daughter aged 11 and son, aged seven, who both started displaying symptoms last week.
When she went online to book tests, she was told the nearest were several hours away in Oldham, Greater Manchester.
She eventually managed to get her children tested at Ysbyty Glan Clwyd, but staff there told her they were "only to test where absolutely necessary".
"It's frustrating," said Ms Massey.
"We're following the guidelines, but people seem really reluctant to allow us to have a test.
"And until we do, the children can't go back to school and I can't go back to work."
A Serco spokesman for the Abercynon site said: "It was closed for a short period because of operational issues but it reopened and the backlog has all been cleared."
A Welsh Government spokeswoman said: "The problems people have been experiencing when trying to book a test are directly related to the ongoing UK-wide issues with the Lighthouse Lab system, which we urgently need to see resolved at a UK level.
"The health minister [in Wales] has repeatedly raised this with the [UK government's] secretary of state for health.
"We are moving as much NHS Wales testing capacity as we can into areas where testing is needed the most, as well as taking urgent action to switch over testing facilities to Welsh laboratories to further increase capacity while the UK government resolves these issues with the Lighthouse Lab system."