I see at least one problem with this. Adjusting the difficulty (or miner rewards, or something similar) works much better one way than the other.
I'll assume a mining system similar to Bitcoin. If the value of your coin gets too high, sure you can devalue it by making it easier to mine and dumping more coins on the market. (Already there is an issue that you'll have to get everyone to agree that the mining adjustments are being made based on a "true" market price that isn't subject to manipulation.)
But what do you do if the value is too low? Making it harder to mine will slow down its inflation, but does nothing about the coins already out there. Unless you are going to take away people's coins or buy them back somehow, this will be a very slow way to revalue your currency. It may not be able to keep up with the market.
To put it another way, if you control the supply, you can drive the price down as far as you like. But to drive it up, there has to be demand.
Furthermore, as you make mining less rewarding, miners will leave. This hurts the security of your coin and makes a 51% or similar attack easier, and will tend to reduce demand further.
The usual approach for making one currency track another is with a peg: a market participant with extremely deep pockets (such as a government) announces that they will buy or sell unlimited amounts of the coin at the desired rate. If they do so, the price cannot fall above or below this fixed rate. But if the market starts to doubt their willingness or ability to maintain the peg, you may see a run on the bank.