The best way to do this is to list the 4 children from oldest to youngest in the “survived by” area of the obituary.
For example, you might state, “she is survived by her four children, Child 1 (spouse); Child 2 (spouse); Child 3 (spouse); and Child 4 (spouse).”
Or, if you wish to incorporate the father’s names, you could also state it this way:
“she is survived by her four children; her son/daughter with X, Child 1 (spouse); and her children with X, Child 2 (spouse), Child 3 (spouse), and Child 4 (spouse).”
I hope that is helpful to you. Please also accept our condolences on the recent loss of your mother.