Why is the English word 'second' latin based but other numbers aren't?

EtymOnline explains what happened in their entry for "second":

Replaced native other in this sense because of the ambiguousness of the earlier word.

Of course, we still have "other" (but it is no longer synonymous with "second").

Similarly, another, less ambiguous word (quarter) was introduced, as opposed to the original "a fourth" (which is easily confused with 4th).