I think you missed the point.
Since it is a government-run lottery (and a monopoly to boot) and the proceeds are specifically designated for school funding, those who do not care to be associated with the operation, either on religious or political grounds, have no escape other than to take their children out of the public schools. Furthermore, the government does not require you, by law, to buy a lottery ticket, but it does require you to send your children to a school recognized by itself.
Finally, it is rather silly to compare your "right" to buy a lottery ticket with your "right" to educate your children in the way you see fit. No one really cares if you gamble. If you really want to, you can zip over to Cherokee or up to Atlantic City. But if the government runs a gambling operation as monopoly and you are completely unable to opt out of the association, the government has impinged on your freedom.
You are arguing convenience against necessity and that boat won't float.
In short, if you don't like it -- get your kids out. If you can't afford to, then you should have thought of that before you got yourselves pregnant and that's the fault of nobody else but yours.
I'd also like to comment on your use of quotes while typing the word right. By using those quotes, are you insinuating that buying something in a legal marketplace -- a lottery ticket in our example -- is somehow not a right?
Am I to assume that in your mind, it must be written somewhere on legal parchment or an ancient relic sitting in the National Archives for something to be a right? You may find it "silly" that one individual's desire to purchase a lottery ticket is comparable to another's desire to choose particular avenues of education. But to each, their desires are important to them individually. You cannot compare the value of both and decide what is more or less important. Freedom works both ways.