Lynsey Dent, of Cookridge, said personalising her children's shared grave in the churchyard at St Chad’s, Far Headingley, has brought her comfort during "overwhelming grief."
Lynsey, 41, has launched a petition calling on the Church of England to compromise and allow some personal ornaments on the grave.
Her daughter Ellie Mae Brownutt was just six years old when she died from Batten's Disease in May 2015.
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Ellie Mae's family decorated her grave with ornaments including metal flowers and butterflies along with 30cm high Winnie the Pooh and Tigger figures made from stone.
Ellie Mae's brother Caleb - who also suffered from Batten's disease - was buried with his sister after he died aged nine in November 2019.
Lynsey said that at the end of 2020, lapsed rules governing churchyard regulations were strictly enforced by the Anglican Diocese of Leeds
Families were asked to remove all ornaments and potted plants, except for one sunken vase as decoration.
Lynsey said: "When you lose a child you don't lose your maternal instinct, which is to look after them."
"When you physically can't care for them any more, the only thing you can do is look after their resting place and you want their resting place to be personal to them.
"I believe it really helped my mental health to be able to do that after Ellie Mae and Caleb passed.
"I'm wanting them to rewrite the rules with some compromise in them."
Lynsey's petition on change.org is called 'change the heartbreaking regulations for the resting places of babies and children.'
It has won the support of 2,724 people since it was launched in early January.
Lynsey wrote on change.org: "The regulations are in my opinion harsh and heartless to the needs of grieving parents, family and friends, including children, who have lost their siblings, cousins and friends.
"The ability to leave ornaments and see the pretty items others have brought has been a source of great comfort to me personally in my overwhelming grief. "
Lynsey has also written to Archbishop of Cantebury Justin Welby and Bishop of Leeds Nick Baines.
She said she was not aware of the no grave decorations rule when she chose the plot at St Chad's and said the decorations had not been flagged up as a problem before December 2020.
Lynsey said she is grateful that the church is allowing an image of Winnie the Pooh to be engraved on the children's headstone, which has yet to be put back in place after an inscription for Caleb was added.
Mark Hill QC, Chancellor of the Diocese of Leeds, has given permission for Winnie’s image to be cut into the headstone.
Lynsey said: "I know of lots of other parents in my situation who have lost children and it's a really big issue for them that they won't be able to decorate the graves."
Batten's disease is a rare genetic disease that causes loss of all abilities, from sight, to walking, speaking, and eating.
A spokesman for the Anglican Diocese of Leeds, said: "This is a terribly sad situation. The death of any child is a source of great sorrow and the Bishop of Leeds has extended his personal sympathy to Mrs Dent and her husband for their particularly tragic loss of two little children.
"Our churchyards contain the love and grief of many parents and the wider family.
"These issues are both a pastoral and a legal matter, the bishop has to ensure the needs of all parties and the law are upheld.
"Codes of good practice are not a matter of personal discernment or individual taste, but exist caringly for everyone.
"In this matter the local Parochial Church Council made a general request for people to respect both the Churchyard Regulations, and the feelings of others with loved ones buried within the churchyard.”