Harry and Cody Churchill, aged three and 21 months, both died from epidermolysis bullosa (EB) within days of each other in 2013.
But toys and mementos from their grave at Poole Cemetery in Dorset were found damaged.
Their mum Steph Green said the shocking incident took place before what would have been Harry’s 10th birthday.
Dorset police are now appealing for witnesses or anyone with information to come forward.
Steph said: “I just want my children to be able to rest in peace and they can’t do that, it’s disgusting. For someone to come along and do that is just awful.
“They suffered enough when they were alive and they should not have to suffer any more.
“All I want is for someone to come forward and hold their hands up and say sorry, I just want answers.”
Inspector Phil Swanton of Dorset Police, said: “This is clearly a despicable and senseless crime and has caused
considerable upset to the boys’ family.
“We have launched a full investigation to identify those responsible and are carrying out a number of enquiries.
“I would urge anyone who witnessed any suspicious activity or has information as to who committed this offence to contact us.
“I would also urge those responsible to look into their conscience, do the right thing and come forward.”
Charity Debra estimates that around 5,000 people in the UK have the rare condition, which causes the skin to become very fragile and any trauma or friction can result in painful blisters for sufferers.