Persuade the liege to go to war for me on one of the claims

When you hover the mouse over the vote count, it'll tell you who's opposing (more like, not voting for) the vote. Not all voters have the same weight, some count more than others and you can see that here. Concentrate on the bigger voters and those who have a least negative attitute towards you. If the opinion is not too negative, a simple honorary title could make them vote for you (+10/+15). After that, try having them educate your child (+20). If money is not an issue, a gift I think adds +20. Or if the vote is important for you and there's a voter that has a heavy vote, you might even try giving them a land. Also maybe they have a claim on a title, well, if you press that claim it's an automatic +100. Another thing you can do is select him/her to your council. Check their current ambition, if it's getting married, arranging that marriage I think adds relation to you too.

I would go with option one. You say that it leaves you less profit, but that is only partially true. Since you will eventually die and play as your heir, all of that money will drop right back into your pocket. It is possible that your heir will waste some of it, but not a large amount. Most of the money he earns will go back into his properties, and so that gold will end up benefiting you in the long run.

As an additional bonus, if/when your heir wins the war, he will get money and prestige from your non-heir vassal.