I want to apply for HDB flat with one of my children as part of my family nucleus, what to do if ex-spouse refuse to share care and control of one children?

Where custody, care & control decisions are concerned, in the absence of agreement between parties, the Court has to make a decision with the welfare of the children in mind and NOT because of your interests (i.e. your intention to apply for an HDB flat). If your ex-spouse does not agree with shared care & control, you will need to apply to Court to vary the existing Order of Court and explain to the Court why a change in the care & control order is in the interests of your child.