The Brain's moved to Dingwall in 2011 on a student visa of mum Kathryn but the specific type of visa was then abolished.
During their time in the UK, both Kathryn and husband Gregg have secured jobs while son Lachlan, who is now 7 has learnt Gaelic as his first language.
The Home Office has told the family they need to leave the country but on Monday they were given a last minute reprieve.
They now have until 1 August to meet the criteria to stay in the country however they have been banned from working in the meantime.
During the next two months the family now need to show they can fully support themselves however they say the Home Office is setting them up to fail.
Mr Brain said the mood within the family was currently "somewhere between elated a furious".
He said: "We're not sure how to take it.
"I'm grateful to Mr Brokenshire for giving us the extension but that gratitude is tempered by the fact that I am - as a direct result of home office actions - homeless, unemployed, my passport remains confiscated, they have said they will be writing to the DVLA recommending that our drivers' licences be cancelled and that consideration has been given to freezing our bank accounts."
The family say they are only getting by through support from their church and the local community.
Their case has been supported by First Minister Nicola Sturgeon while local MP Ian Blackford has been campaigning on their behalf.
Ian Blackford said: "I find it utterly incredulous that Home Office minister James Brokenshire has decided to extend the Brain family's right to stay in their home in Scotland but refused to grant them the right to work.
"How does he expect Kathryn, Gregg and Lachlan to make ends meet until the beginning of August while the UK government refuses to allow them to work?
"Both Kathryn and Gregg have secured jobs in the local area, which would benefit the local economy and allow them to continue the enormous contribution that they have already made to life in the Highlands.
The Home Office confirmed it had granted the family a further two-month extension to a grace period it was previously given, but said evidence of a relevant job in line with immigration rules had not been provided to date.
It said an application for the family to remain in the UK would be considered if submitted during the grace period.