lol yea she worked through claudius and nero.... wife of (and niece of... yuck yuck yuck) claudius and mother of nero gives you some kind of power.
her political abilities are also visible in the patron/ client system she had going. so she had a beneficial relationship with the army because of the great respect they had for her dead father germanicus and mother agrippina the elder- she reciprocates by building a veteran's colony in ad 50 (where retired army people can live and farm) in cologne, germany. she has connections to burrus, who's the praetorian guard because she suggested he be elected prefect to claudius. (so another person she can influence). also patron of the freedmen i.e. pallas, which leads her to becoming claudius' wife because pallas suggests her as candidate for wife. also, obviously able to influence the running of the principate through claudius and later, nero.
so basically, she had political abilities of manipulation, finding ways of imfluencing people even though there arent any official political roles for females by maintaining connections to those in power.
according to barrett, although the way she used her political abilities were unethical i.e. also knocking off any enemies and rivals through accusing them of treason and stuff like that, she can be admired for the ingenuity and political abilities she had to gain power within a patriarchal world.
evidence for her political abilities can be found in tacitus and suetonius (two of the 'best' ancient sources on aggie).
omg, i think i have verbal diarhoea (and i can't spell that word ><) does that help?