There seem to be three logical possibilities:
- All the sources you have seen talking about the etymology of "second" and how it replaced the Old English cognate to other have neglected to mention an Old English word cognate to zweite.
- Old English lost its word cognate to zweite.
- You are mistaken in thinking that it is "almost certain" that zweite is inherited from common West Germanic.
I'm pretty sure the third is true.
There was no OE ordinal word built with the "two" root
Like the ordinals for ‘1’, those for the numerical value ‘2’ are all suppletive forms. There are two different lexemes which are employed for ‘second’.
OE ÆFTER ‘subsequent, following’ is a comparative formation containing a root which otherwise survives in the adverb OE EFT ‘afterwards, again’. In its weak inflected form æft(e)ra, it is sometimes used as an ordinal. In most instances, the implication ‘following’ cannot be completely interpreted away, and the strictly ordinal sense is implied by the contextual reading rather than by the primary lexical meaning of ÆFTER [...]. The use of ÆFTER with an exclusively ordinal function [...] is therefore rare.
OÞER may be the default lexeme for the ordinal ‘second’. The use of this lexeme for ordinal number assignment is older, since it is attested in other Germanic and in some Indo-European languages, too. Like PDE other, the expression is used in a wide variety of senses and implications, such as ‘another’, ‘different’, etc., and instances where OÞER is used clearly and exclusively as an ordinal are again rare (Cardinal Numerals:
Old English from a Cross-Linguistic Perspective, by Ferdinand von Mengden, pp. 122-123)
The "other" ordinal is attested across West Germanic languages
Paul (2007:232) points out that ander is the usual ordinal number for 'second' [in German] until the 16th century when it is replaced by zweit. (Quantifying Expressions in the History of German, by Dorian Roehrs, Christopher Sapp)
The trend mentioned in this quotation of zweit- taking over some of the functions of ander- in German over time is evidence that the "twoth" construction is an innovation in the West Germanic languages that have it, rather than something that existed in the common ancestor of German and English and then was lost in the latter.
It's unlikely that Old English lost an inherited "twoth" ordinal
The etymological argument against supposing the twoth-type ordinal goes back to common West Germanic is about the same as the one underlying the textual criticism concept of "lectio difficilior potior." It's more likely for an irregular ordinal such as "other" to be replaced by a regular ordinal like "twoth" than the reverse. The "twoth" word is, as you say, present in some modern West Germanic languages, but it is apparently not attested in Old English or older German texts. If you suppose it existed in common West Germanic, you have the problem of explaining why it was lost in Old English and Old High German (and how it was transmitted to modern German).
Words like twadde, tweede, zweite are not very strong evidence for reconstructing a "twoth" word in the common ancestor of West Germanic because they are all clearly composed of the "two" morpheme and the usual ordinal suffix "-th." It is not very surprising if it turns out this kind of regularized ordinal form is an innovation that replaced an inherited irregular ordinal form in several languages that are all geographically fairly close to one another, like German, Dutch and Frisian. And that seems to be what happened.