From Latin se-natus, "self-born," in earliest times probably a group of matrones or tribal mothers thought to be reincarnated in their daughters by matrilineal succession. The later patriarchal gods also claimed to be "self-born," like Ra in Egypt. Providing any god with a mother implied that there was an older, greater female authority over him-- a self-defeating idea for patriarchal thinkers.[1, p. 902]Senate is not related to natus, and does pretty certainly not mean "self-born". How do we know this?
- natus changes to gnatus with every other prefix we know it to occur with, c.f. cognatus and pregnas.
- senatus and natus are not of the same declension. Applying a prefix does not change the declension of nouns in Latin. Sometimes, different nouns have a few forms cooccuring, c.f. anus (anus, ring) and anus (old woman), or datus and datum, both of which have forms that coincide and forms that are distinct. Thus, senatus and natus being similar in the nominative does not prove that they originate with the same word, and their not being similar throughout the paradigm indicates they very probably are not.
- se- is not used very often for that kind of construction
- We know what it actually derives from - senectus, from senex. Senex signifies old, senectus is a collective noun for old persons. Thus, the senate is basically an assembly of elders.
- We know the greeks translated it as gerousia, which also signifies an assembly of old people.
Alas - or maybe rather, fortunately - Latin reference grammars will not go about listing every thing that isn't permissible in Latin. Thus finding a concise source for any of the claims above is rather challenging, as these claims are negative rather than positive and reference grammars generally describe what is possible.
It should be pretty obvious Walker just tried her hand rather ineptly at etymology in order to prop up her hypothesis, which is that Indo-European culture had been, rather recently, predominantly a matriarchy.
 Barbara Walker, The Woman's Encyclopedia of Myths and Secrets