...'supporting' his brother's... I disagree with angry_hermit's suggestion on the first one - his sentence changes the meaning of the original, which is fine. Strangely enough, both versions (continue/continuing) sound ok in that first example.

That first one has a sentence structure that might seem odd to a native speaker. Try this instead: He has committed his government to the path of economic reform. As for the second one, it would be more natural to say this: He has committed himself to supporting his brother's children.