can't open the data because i use an earlier version, in any case i guess you can do it in two steps (I am assuming there are no parentless children or childless parents) :

*step 1 : first link child with father

use parents.dta

sort id

save parents.dta, replace

use children.dta, clear

gen id=father_id

sort id

merge m:1 id using parents.dta

save children1

keep if _merge==3

save children_f

*step 2 : link fatherless children with mother

use children1,clear

keep if _merge==1

drop _merge id

gen id=mother_id

sort id

merge m:1 id using parents.dta

keep if _merge==3

append using children_f /*put things together*/

save matched

Looking at the data, I would suggest that the most simple way is to merge twice: First merge parent work data against the mother_id of the children. Then rename and merge again against father_id. This will give you a data set of the format

child_id mother_id works_status_mother father_id works_status_father

Does that solve your problem?

Thank you so much for all your assistance. I have managed to carry out this task with the directions provided above. Very much appreciated.