A while ago I was asked the same question with solution preferably in python and I came up with this:

Get Orange-Bioinformatics python library:

pip install --user Orange-Bioinformatics

Get database of go terms:

wget http://purl.obolibrary.org/obo/go.obo

Produce a table with two columns, child_term, parent_term:

python

import Orange.bio.obiOntology

obi= Orange.bio.obiOntology.OBOOntology('go.obo')
all_terms= obi.terms()

fout= open('go.obo.paired.txt', 'w')
fout.write('child_term\tparent_term\n')
for t in all_terms:
    parents= obi.super_terms(t)
    if len(parents) == 0:
        fout.writet.id + '\t' + 'NA' + '\n')
    else:
        for p in parents:
            fout.writet.id + '\t' + p.id + '\n')
fout.close()

len(all_terms)
quit()

Output table file looks like this. It should be fairly easy from here to get all children of a parent or vice-versa using e.g. grep:

child_term      parent_term
GO:0000001      GO:1902589
GO:0000001      GO:0071840
GO:0000001      GO:0007005
GO:0000001      GO:0051641
GO:0000001      GO:0016043
GO:0000001      GO:0044763
GO:0000001      GO:1902580
GO:0000001      GO:1902578

Hope this helps.

I think the R package GO.db can do this. Alternatively, in perl, you can use the go-perl library.