Can you control what ore a drill harvests when it's placed over multiple ores?

No, you cannot.

Two ways of dealing with the fact that some coal will be included with the uranium are:

• Placing the uranium drill in such a manner that it does not touch coal. Note that, when you place down the miner, it shows a square around it, indicating what area will be mined.
• Feeding the output to a belt and having a filter inserter on it, or somesuch (feeding it into a provider chest and make the robots deal with it, feed it into a chest and have a filter inserter extract only the uranium ...)

Alternatively, you could fix this problem not at the start, but at the end: feed the entire belt into your centrifuges, and have a filter inserter pick out all the coal at the end. The centrifuges will only pick out the uranium.

It is now (0.16.17) also possible to set an output filter for one output lane of a splitter. This will put only items of that type on that belt, everything else on the other. Left click on the splitter to control its settings.

This is similar to the filter insert approach except that it achieves maximum throughput with a single splitter. With a filter inserter you might need multiple inserts to get the same throughput.