Here's an hypothesis to follow up. Perhaps it comes from Gk. topos, place, via the verbs topple and tottle. The etymological pedigree would then be:
topple becomes tottle, which gives rise to tottler, which would naturally change in pronunciation over time to toddler. And then the verb toddle comes from the noun toddler, not the other way round? Just an idea.

Totītle (tǒtīt'l) v. i. 1. To walk in a wavering, unsteady manner; to toddle; to topple.
[imp. & p. p. Tottled (tǒt"t'ld); p. pr. & vb. n. Tottling (tǒt"tlĭng).] Webster's Revised Unabridged Dictionary, published 1913 by C. & G. Merriam Co.

top·ple \ˈtä-pəl\
Etymology:frequentative of top
intransitive verb: to fall from or as if from being top-heavy
transitive verb1: to cause to topple

In any case, whether the above is possible or not, the OP should remember that the woman is always right (even when she's not!).