Mr Tweed, 61, who went on to become a unionist politician after his sporting career which included four caps for Ireland, died in a road crash in Co Antrim last month.
His stepdaughter Amanda Brown said he was a paedophile and a violent thug, and challenged politicians who put out complimentary statements in the wake of his death.
Mr Tweed was convicted of child sex offences in 2012 and sentenced to eight years in prison.
He was released in October 2016 after his convictions were quashed by the Court of Appeal in Belfast.
Ms Brown said some of the sentiments in the statements were “massively disrespectful to all victims of abuse”.
“When people are passing comment about this great man after knowing what he was convicted of, to still support him, that’s the message that they’re giving out to other victims,” she told BBC Radio Ulster’s Talkback programme
Ms Brown became Mr Tweed’s stepdaughter when she was four after her mum became involved with him.
She said outside the home he was a very well-respected man, particularly with his rugby career, before becoming an elected councillor for the DUP which she said gave him “a bit of status”.
Mr Tweed went on to join the TUV, and served as a councillor in Ballymena.
However Ms Brown said he was different at home.
“I found it quite confusing at times … particularly when we were at a rugby match, how he was amongst his peers then, and you’d have heard him laughing and joking, and he’d have been nice and bought us bottle of juice and packets of crisps, we were involved and it seemed like very much a family occasion,” she said.
“But when you got home it was a completely different matter, and the slightest thing that could have happened through the day would have been recalled … if it was something that I would have done, I would have got yelled at, and it normally escalated into domestic violence as well for my mum.
“I can’t speak for my mum but as a child witnessing that, it was horrific.
“We never seen him hit her but we heard it and hearing the thumps and the thuds and hearing her yells, and having these images in your mind of what potentially was going on.
“Almost always afterwards he would throw her into our bedroom and have her tell us it was her fault, that she deserved the beating that she’d just got.
“He wasn’t physically violent to me, I have witnessed him being physically violent with one of my other sisters … we were on holidays and we were in the villa beside them, they were connected, I had come walking up the path to go to my villa and he was literally throwing my sister across the room, and I walked into their villa and took her out of it at that point.
“She was only a child, in or around 11.”
Ms Brown said she felt “peace” when she heard he had died.
“You were always concerned he would show up somewhere and you were always concerned about what he could do,” she said.
“But also peace that he can’t hurt anyone else anymore.”