Sally Ann John, who disappeared from Swindon, aged 23, in 1995, had been working as a prostitute.
On Thursday police arrested three men in their 50s on suspicion of her murder.
"Every day is difficult without Sally Ann and I appreciate the understanding I have been shown," said Lesley John.
In a statement released through Wiltshire Police, she said: "The police have been keeping me informed of progress with the investigation into Sally Ann's disappearance and the arrests yesterday give me hope.
"I feel it is important that the police are able to continue to investigate without speculation from anyone and I hope that the community will support me in this."
The trio, including two men from Swindon aged 50 and 52, and a 52-year-old from Chippenham, are still being held on suspicion of kidnap and murder.
Sally Ann's disappearance was initially classified as a missing person but police launched a murder investigation in 2014.
She was last seen on Aylesbury Street on the morning of Friday 8 September 1995. Her body has never been found.

30 November 2016 Last updated at 01:55 GMT
She's been telling the BBC about working on her debut album and teaching jazz and the sax to young kids in the Namibian capital Windhoek.

Dublin side Bohemians visit Brandywell Stadium on Friday night in the first home game since Dundalk supporters were attacked earlier this month.
Fans, residents and club officials marched from Lecky Road to Brandywell.
Club director Denis Bradley said it was a symbolic gesture to prevent further trouble and 500 people took part.
"This is a battle we will win, this is a battle we have to win, maybe not immediately but we are very resolved," he said.
Derry City's FAI Cup semi-final defeat by Dundalk FC was marred by trouble outside the ground.
A teenager suffered head injuries and a Dundalk supporters' bus was vandalised.
Police said they have been liaising closely with the local community and the club in preparation for Friday night's match.
Ch Insp Alan Hutton said: "There will be an appropriate policing operation to ensure the safety of all supporters attending, as well as minimising any impact on local communities.
"I would encourage all supporters to come and enjoy the game and respect the local community.
"I would also like to acknowledge the excellent work carried out by the local community and Derry City football club in preparation for tonight's match."
Derry City added that the trouble by a "group of youths" was not typical.
"There is a group of youngsters, we don't know where they are from or who they are, who appear to be using these occasions to misbehave," Mr Bradley said.
"Derry City are saying tonight: "Not in our name" and the local residents are joining us to say: "Not in our area" are you doing these things."
The mother of a woman who went missing 20 years ago and is believed to have been murdered has said the recent arrests have given her hope.
[NEXT_CONCEPT]
Suzy Eises is a saxophonist from Namibia who has shared the stage with South Africa’s Jimmy Dludlu and other African artists.
[NEXT_CONCEPT]
Derry City Football Club has held what it describes as "a public act of defiance" to show disapproval at attacks on visiting fans this season.