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“to’ is complex because it has different uses – sometimes the hardest words are those that look simple. In truth, the best way to try and get this right is often to “learn phrases” as it is one of those areas that the “rules” are so complex that they end up confusing you. In your example, you cannot say: “global programme to educating people.” If you want a grammatical answer, I’d say that in “global programme to educate people..” “to educate” is an infinitive of the verb, whereas in “the key to making this happen..”. the “to making” is a preposition followed by a verb meaning the “to” bit belongs to the noun and not the verb.