Report by ITV Calendar journalist Chris Kiddey
Sabrina and Tony Edge, from Driffield, contacted the Kurcher family in Ukraine two weeks ago, when they were forced to flee their home after Russia's invasion.
Mrs Edge and Liliia Kucher quickly became friends after connecting online.
But, while the government sponsorship scheme for refugees is now live, the Edge family say they are no closer to getting the Kuchers over to the UK.
Mrs Edge said: "I am just so frustrated, as some responses I have received say that I may not get a response for 20 working days.
"How many people could die in that time? How far would the situation have escalated by then?"
Mrs Edge said she has registered to be a refugee host via the Homes for Ukraine website and she and her husband have contacted countless organisations to establish a timescale for when the families can unite.
She said: "When the website was announced to be live yesterday, we were overjoyed to finally get the ball rolling after two long weeks worrying about Liliia and her family.
"We have even received a email from Priti Patel, giving us standard information about the scheme, but it is nothing that we don't already know, and we think that the Government is simply stalling."
Michael Gove, Secretary of State for Housing, Communities and Local Government, said in a statement: “We want to minimise bureaucracy and make the process as straightforward as possible while doing everything we can to ensure the safety of all involved.
"Sponsors will therefore be required to undergo necessary vetting checks, and we are also streamlining processes to security-assess the status of Ukrainians who will be arriving in the United Kingdom.”