What’s wrong with this?

"make" can be used with another verb as a causative, for instance
"I made him cut the grass."
If the object is topicalized then we end up with the second verb immediately following "make", but I don't see anything wrong with this.
I made him cut the grass.
He's the guy I made cut the grass.
I made him do the dishes.
He's the guy I made do the dishes.

"Hey, you're that goofy kid that Sandra forces to do crazy stuff!"

"Hey, you're that goofy kid Sandra gets to do crazy stuff!"

Is it more palatable as

"Hey, you're that goofy kid whom Sandra makes do crazy stuff!"

?

I have to go with Anonymous.

There is a 'that' missing which puts it all into perspective. My guess is that this is not English, but American ("kinda like you know like what I mean LIKE") and the correct form of this sentence would be

"Hey, you're that goofy kid that Sandra makes do crazy stuff!!"

even though this is still not the greatest use of the language...

Isn't this one of those "gardenpath" utterances?

A garden path sentence is where you have to reparse. For instance
"The horse raced past the barn fell"
You interpret "raced" as the past tense of "race"... until you get to the last word, when you have to go back and reinterpret "raced" as a past participle.

"You're that goofy kid"... fine
"You're that goofy kid Sandra"... could be interpreted as "You're that goofy kid (named) Sandra"
"you're that goofy kid Sandra makes"... reparse as "You're that goofy kid (that) Sandra makes..."

Adding "that" might make the sentence clearer, but such a "that" is optional. The sentence is correct as is, albeit somewhat colorful. If it's ok (grammatically or logically) for someone to make someone else do something, then identifying that "someone" in the manner in question is ok.

I assume that "Sandra makes someone do something" doesn't bother you. "Sandra makes someone do crazy stuff" is also ok, right? "crazy stuff" is certainly colorful, but not ungrammatical. Sandra makes a goofy kid do crazy stuff" should also be ok, right? So you see the goofy kid and say: "Hey, you're that goofy kid!" (Which goofy kid?) "that goofy kid that Sandra makes do crazy stuff." Take away the optional "that" and you have the original sentence.

PS - it isn't really a garden path sentence. In order to misconstrue "Sandra" as the name of the goofy kid, there would have to be a comma before Sandra.

The addition of 'that' is grammatically incorrect. The kid is the object of "Sandra makes...", so an object pronoun is needed, and since the kid is human, it should be 'whom'. That's how we get:

"Hey, you're that goofy kid whom Sandra makes do crazy stuff!"

(Oddly enough, the use of 'goofy' and 'crazy' cause the 'whom' to feel out of place, since they are rather informal and just about the only time anyone remembers to use 'whom' is in formal writing. However, this is the grammatically correct, if not stylistically consistent, version. :) )

There is nothing ungrammatical about using "that" with a human. "Human" is not a grammatical case in English.