Learn English – The Color red or the Red color

The easiest way for a native speaker to distinguish between a descriptive and classifier adjective is to attempt to intensify it. Consider the following:

• The old train
• The very old train
• The steam train
• *The very steam train

While you can intensify descriptive adjectives (the very old train), you can't do it to classifiers, at least without some kind of strangeness.

Another test that can be applied is paraphrasing the noun phrase as a sentence that uses the verb be. In the example above, you can say the train is old, but not the train is steam.

You can also try to fit in another classifier before the one you're trying to test:

• The old teacher
• *The math old teacher

English doesn't allow for this type of structure if the adjective is descriptive. However, this is a one-way test only - you can't test whether something is a classifier because you can have a classifier followed by another:

• The revolving doors.
• The automatic revolving doors.

Of course, this is less straightforward for a non-native speaker, who won't necessarily have that intuition that tells you whether a phrase is grammatical or not.

Some combination of the above is probably going to work for you, with the easiest being the intensifier.

For your specific example, let's apply some tests:

• "an old political idea"
  the political idea is old - descriptive

• "latest educational reform"
  The latest reform is educational - descriptive

• "leather dancing shoes"
  The dancing shoes are leather - descriptive

You can find out more by searching for epithet vs classifier tests, which produced some of the tests I've noted above.

The writer maybe sees push open as a phrasal verb, like put on. Phrasal verbs can be used in two ways:

1) She put the dress on
2) She put on the dress.

Your sentence matches form 2). I cannot find any dictionary evidence to confirm that it is normal to use push open as a phrasal verb, but this NGram indicates that quite a few writers use this form.

Here are a couple of examples:

When you've finished putting beads on all the pins, open the big (#3) safety pin and use the nail file to push open the little loop-the-loop at the end of it My best friends and me

Silence promises danger not peace, for always the sounds that push open my door or your door, are remembered as coming out of nothing. In the shadow of sharpeville