The former UUP deputy mayor of Derry and Strabane Council was disqualified from council for 15 months after a decision by the local government watchdog on Tuesday.
Mr Hussey has three convictions for drink-driving offences and was banned from driving for five years in 2016.
His disqualification begins on Tuesday, July 16.
Martin Gallagher, whose son Martin Jr was killed by a drunk driver in 2009, said he was “not happy at all” with the sanction.
“He should have got a longer disqualification – he was caught drink-driving three times,” said Mr Gallagher.
“If we hadn’t taken this complaint he would still be a sitting councillor.”
Derry student Robert Bradley was killed along with a friend by a drunk driver in Nottingham 18 years ago.
His father Robert Bradley said the family “feels highly insulted” that Mr Hussey was elected as Derry City and Strabane District Council’s deputy mayor.
“He should have not been able to take up a senior position in council,” Mr Bradley said.
“Our position is not about politics – it’s about road safety and drink-driving.”
“We don’t want to see this happen to another family in this city.”Derry City and Strabane District Council said it was not responsible for dealing with the complaints.
The Northern Ireland Public Services Ombudsman (NIPSO), which imposed the disqualification, said it would publish its decision in writing soon.
“It will explain in more details why a 15-month disqualification was considered to be an appropriate sanction,” it added.
After Tuesday’s hearing Mr Hussey’s solicitor said he would appeal the disqualification.
Depending on the outcome, Mr Hussey may have to be replaced on Derry City and Strabane District Council and his party would have to co-opt a replacement.
He was re-elected as a councillor for the Derg area in the council election in May.