Translation:I do not do what they want, but what I want.
Yes, and that would be a better English translation for this sentence than the one used here. I would actually translate it as "but rather what I want".
The difference is that אלא is used when an alternate is being proposed (i.e. 'but rather'), where אך is just for negating. So אך would not normally be used in that sentence.
Why is the direct object marker not used in this sentence? Is using it an option without altering the meaning?