If you are living with the father of the two children then there is no legal avenue for you to obtain an order of child support from the father.
The law assumes that if both parents are living together than both are providing financial and emotional support to their children. If this is not the case you would be expected to have separate residences.
In that case, you would file a petition with the court and a determination would be made regarding legal custody, physical custody, child support to be paid to you, and visitation rights.
The father's ex-wife may be receiving child support from him, but this cannot prevent the father from paying child support to you for your children. It is because he is residing with you that you cannot ask for child support.
If you lived apart, the fact that he is paying child support for other children would be taken into consideration when calculating the amount of support you would receive, but this would never bring the amount down to zero where you would receive no support. The more children a father is supporting through child support orders (physically residing with none of them), the less he will be expect to pay for each one.
His total child support payment, however, will be higher than if he was only support one child versus two or two versus three.
So the only way to obtain child support is to leave him (or have him move out either voluntarily or by obtaining a restraining order and court order if these are appropriate.) As long as you and he reside together you cannot petition the court for support from him.
Please let me know if you have any questions about this.