Dismissive people can be frustrating, tiring and counterproductive. Be it at work, with family or in friendships, you want to be listened to, whether you're agreed with or not. A calm, measured approach works best, as an angry and forceful response to their dismissive behavior will probably only compel them to ignore you further. Whether they mean to be dismissive or not, remember to stay calm and follow a few simple steps in order to get their attention.
Decide on what it is that specifically bothers you. Yes, they're dismissive, but what is or is not getting done as a result? If your boss doesn't listen to your suggestions at work, the solution would not be to offer even more suggestions in a forceful manner. Rather, it would serve you better to explain the merits of employee feedback in general. At first, focus on the big picture, not the minutiae, and why he needs not to be dismissive. (Reference 1)
Keep your cool. As mentioned, don't press harder for your voice to be heard. The dismissive person knows that you wish to get in your two cents, but she is not listening. That said, getting angry or in her face won't serve you well. As the saying goes, you catch more flies with honey, and the more calm and diplomatic you are, the better your chances are of being listened to. You simply need to refine your approach.
Ask his opinion on a given matter. Your point of view did not interest him initially, but if you can get him to tell it the way he sees it, he may jump at the chance. Even if you don't agree with him, you've gotten off to a good start by getting the conversation rolling, meaning that you will finally get an opportunity to have the floor when he's done. (Reference 1)
Show specifically how your ideas work; actions are often more effective than words when it comes to getting through to someone who is dismissive of you. If you're making no headway telling your father that aerating the lawn is best for the landscaping, do so when he's away. Eventually, he will see improvement, and you can then reveal what you did. Just be gracious about it and avoid any "I told you so" sentiment.