1) on your father demise your mother , 3sons would be legal heirs
2) since you are willing to give NOC , execute relinquishment deed in favour of builder then builder should have no problem in transferring flat in your mother name .
3) you are also willing to execute indemnity bond to indemnify the builder against all claims made if any
4) builder is not entitled to ask for some percent for transfer of flat in your mother name .
5) if builder insists obtain succession certificate from court . it wont take more than 6 months .