“And with the income tax amendment, the federal government can take money from the states...”
Actually it takes money from citizens of the states.
“...and withhold it, unless the state does what is required by the federal government. The state won’t get that money back unless the state cooperates.”
If the Federal Government is limited to the powers delegated through the Constitution by the States, what would the States have to cooperate with that they wouldn’t?
Suppose the federal government collected gasoline taxes, but then required the states to implement a state-wide 55mph speed limit in order to get the money back. What would happen? Most states would submit to the will of the feds just to get back that money.
This was done in the 70's to get people to drive more slowly to conserve gas. Nearly all states gave in.