(Many contributions have strings attached. Yours doesn't have to.)
My wild-ass guess (not a political science major) is that voters can be bucketed into the following broad groups:
A: People who vote straight party-line, no matter what. A toad could be on the ticket and they'd vote for it.
B: People who vote for whatever name they most recognize.
C: People who actually study the candidate's positions and make a rational choice.
Generously let's say A=80%, B=17% and C=3% of voters.
Whether or not you get A's vote depends entirely on what letter is next to your name--you have no control. B's vote is expensive because you need to carpet the area with saturation advertising in order for them to remember you when they fill out the form. C is so small that it's probably not worthwhile to do the legwork. So you end up spending tons of money hoping that you can get B to tip the scale towards you. At least that's how it looks to me.
Since the parents is discussing running for local office, I'm not sure why you think party comes in to play. Or perhaps this is a regional thing? In my city, party affiliations are not advertised/listed for positions such as city council, mayoral, parks board etc.