In a judgment of dissolution of marriage or legal separation of the parties, the court may deny support to a party out of the separate property of the other party in any of the following circumstances:
(a)
The party has separate property, or is earning the party’s own livelihood, or there is community property or quasi-community property sufficient to give the party proper support.
(b)
The custody of the children has been awarded to
the other party, who is supporting them.