This answer is long because it can be very difficult for learners to distinguish a) Correct double negative in Standard English, b) Double negative error in Standard English, and c) Correct negative concord in non-standard English.
Direct answer
You are correct, you can say exactly what you mean with exactly that sentence. However, as you can see from the length of this and the other answers, correct Standard English sentences which have double negatives are often misunderstood as errors, dialect grammar, or worse, the opposite of what you mean.
You might want to rephrase your sentence, perhaps along these lines: "I don't want you stuck in one place", "I want you to do something, not be stuck and going nowhere".
Standard English
Standard English, as you will read on the BBC and the New York Times, has "negative polarity", which means that a double negative is actually a positive, though not necessarily with the identical intention as the obvious positive statement. A "double negative" is where there are two negatives in the phrase, although many people use the phrase only to mean a "double-negative error".
The OED says
double negative n. Grammar a syntactic construction containing two negative elements, esp. where only one is now expected in Standard English; either of the negative elements in such a construction.
- I ate simple positive statement
- I didn't eat simple negative statement
- I didn't eat anything negative statement
- I didn't eat nothing double negative which means "I ate something". This is a very rare construction which which emphasises that it is something, not nothing. "I didn't eat nothing, but it was very small."
- I didn't not eat double negative, which means "I ate". This is a very rare construction which emphasises that it happened. "I didn't not eat, but it was so small it wasn't really a meal.
Your example
I do not want you to go nowhere.
This is a double negative, which is absolutely correct in Standard English but is rare. Its meaning is double: a) "you go nowhere", and b) I don't want that. This gives a positive sense, but is subtly different from the positive statement "I want you to go somewhere", and would only be used in sentences such as this: "I do not want you to go nowhere, I want you to go somewhere." As noted in comments, there is emphasis on the nowhere. (Thanks @chrylis) It is often needed to say things like "It isn't zero, but it is very small." One of the most common uses of correct double negatives is in an argument: Bert: "I did everything. You did nothing." Ernie: "I didn't do nothing, I did my share."
Alternatively it is a common error for the more usual sentences:
- I do not want you to go or I do not want you to go anywhere Which means "I want you to stay", or
- I want you to go nowhere which means "I want you to stay here" (but is somewhat awkward.)
Negative Concord in Non-Standard English
Be aware that many native speakers do not speak Standard English.
There are many varieties of non-standard English which have "negative agreement", also called "negative concord", and you will hear "I didn't eat nothing" where standard English has "I didn't eat anything". Many languages have negative concord, such as Russian, Spanish, Hebrew, and the general idea is that the parts of a sentence which are negatable must all agree. Just as in English we have gender agreement -- "She said she herself is tall like her father" must become "He said he himself is tall like his father" -- some grammars require all the variable parts of the sentence to match in positive or negative forms. In Spanish when you negate "Tengo sed también" (literally "I have thirst too") it becomes "No tengo sed tampoco" (literally "Not I have thirst neither"): we add "no" and alter "tambien" into "tampoco".
Amongst the many English dialects with negative concord are Cockney, for example Eliza in Pygmalion says "I ain't done nothing wrong" (Standard English: "I have done nothing wrong" or "I haven't done anything wrong"); West Country (of England) Sergeant Turner in Hot Fuzz: "Nobody tells me nothing" (StdE: "Nobody tells me anything"); African-American vernacular wiki: Jules in Pulp Fiction: "Don't do nothing stupid" (StdE: "Don't do anything stupid"), and Italian-American vernacular, Sonny in The Godfather: "Goddamn FBI, don't respect nothing" (StdE: "Goddamned FBI, they don't respect anything.") (Thanks @Bee and @OrangeDog in comments.)
Unless you are living in an area with dialect grammar, you are probably best advised to learn standard grammar. Certainly all tests and exams for learners of English would give Eliza, Sergeant Turner, Jules and Sonny poor grades.
The Wikipedia article on Double negative covers the variety well.
