Selling tickets for an event through DSP could be so much easier. In the space where you set up ticket sales, there should be a box to check about allowing ticket sales in the parent portal (instead of that being a completely separate setting that isn't mentioned anywhere during setup), just like each class that you set up in a Season has the option of allowing or disallowing online registration, even if you have online registration set up, it's still right there in the class set up. Should be the same for tickets.
Also, if you are NOT able to use a link to sell tickets to parents if you're only selling to parents, that should be mentioned on the page that generates the link! (As in, "get link" then under "only for selling to general public"