"2 other" vs. "other 2"

"And other two places" is not said as far as I can tell. However, if "and" is replaced by "the" it is clear that you can say "other two places"; this has even been the preferred order since the 1820's (ngram); nevertheless, this is not according to the prescriptions, which require that the postdeterminer be placed before the adjective, the trend being largely to follow this rule. "Two" as well as the other numbers belong to the class of the postdeterminers in English and postdeterminers are determiners.

This reference shows the places of the determiners in the noun phrase.
Determiners come first in noun phrases, before adjectives and noun modifiers.

According to this, as "other" is an adjective you must write "two other places", "the two other places". In this ngram you can see that this order is prevalent. There is a very small minority (the other two sides, the other two groups, the other two men) but for these three words this is nonetheless by far the preferred order.