Samantha Baldwin, 42, from Newark, has not been seen since Monday and is believed to be with Louis Madge, 9, and Dylan Madge, 6.
Police say they are treating the case as an abduction.
In a statement, Nottingham Family Court said Ms Baldwin was "considered to pose a risk of harm" to the boys.
It said the children had been removed from her care at a hearing on Monday and had been made wards of court in light of the disappearance.
CCTV images from the same day as the hearing showed Ms Baldwin alone at two locations in Nottingham city centre.
Police have urged B&B operators, hotel owners and those in charge of other holiday properties to be on the lookout for the trio.
Supt Rich Fretwell from Nottinghamshire Police said Ms Baldwin may have altered her appearance.
"Our investigation team are exploring a number of lines of enquiry. There's always the possibility that Samantha could be being harboured by someone," supt Fretwell said.
"We would urge that person to come forward and let us know where the boys are.
"We would also like to appeal to anyone who owns or runs a guest house, B&B or hotel to check your registers and be mindful that the group may be staying under a different name.
"We would also ask caravan park operators and holiday let properties to think about any groups that have joined them since Monday.
"We cannot stress enough the likelihood that Samantha may have changed her appearance and we would like you to keep an open mind."
Two women, aged 62 and 36, were bailed on Wednesday after being arrested on suspicion of assisting an offender.
Two young boys who have gone missing with their mother had been removed from her care on the day they disappeared, it has emerged.