The 32-year-old, of Arbourthorne, was one of 22 people killed when suicide bomber Salman Abedi detonated a device outside the Manchester Arena after an Ariana Grande concert in May.
She had attended with her sister Claire Booth and her 12-year-old niece Hollie. Both relatives are still in hospital receiving treatment for serious injuries.
A statement issued by South Yorkshire Police today on behalf of the family said: "This is an incredibly difficult time for our family and so we ask that we can be left to grieve in peace.
"We know people are concerned about Hollie and Claire. Claire has now received treatment and is physically recovering. Hollie remains in a stable condition.
"It’s important that we are now able to spend as much time as possible supporting them.”
The statement added that while Kelly's body has been brought back to Sheffield, Claire and Hollie remain in Manchester receiving treatment.
It is believed Claire sustained a broken jaw in the blast, while Hollie suffered two broken legs.
Kelly's dad Kevin posted on Facebook: "Claire is doing fine, Hollie is having another operation on Friday and if there is no infection found she could possibly be transferred to (Sheffield) Children's Hospital on Monday.
"Let's hope for that and get them nearer home at last. Thank you all for your messages, they mean a lot to me and Kim (Kelly's mum). We will see you all soon."