"Ik wil niet dat je mij duwt."
Translation:I do not want you to push me.
Phonetically, oe is a simple vowel; that is, it has a single sound, as in the English word 'too'. By contrast, uw is a diphthong; that is, it starts with one sound and ends with another. In this case, the 'slide' is formed by rounding the lips during the utterance. The phonetic samples of these two words that are found at Wiktionary.com may be helpful.
Personally, I find the many diphthongs to be the most challenging thing about speaking and understanding Dutch, and not the grammar. American English has very few sliding vowels by comparison and I was taught not to slide vowels when speaking properly. I find it a difficult habit to break, but break it I must.
It doesn't provide the ‘to’: as you can see, in English ‘push’ stays unconjugated, in the infinitive (‘to push’), while Dutch uses a finite form (‘duwt’). It is a completely different grammatical structure to express the same thing, one that would correspond to a (hypothetical) English ‘I don't want that you push me’.
Using an infinitive structure is simply ungrammatical for this kind of expression in Dutch—if it weren't, the sentence would be ‘ik wil je mij niet duwen’, without any ‘to/te’ because, contrary to English, in Dutch ‘to want/willen’ as an auxiliary verb requires the bare infinitive. The reason why this sentence is ungrammatical is that in Dutch (as in English, for the most part) infinitive constructions (with or without ‘te’) presume the subject to be the same as the main clause, for example: ‘I hope to become rich / ik hoop rijk te worden’ = ‘I hope that I become rich’. English allows you to specify another subject, but many other languages—to my knowledge, practically all other European languages—don't, so you have to express it with a noun clause.
Sorry for the very long explanation, I thought you might be interested in the details.