Try hard to link your Google Map page to get into the 3-pack in search results. Do that and you can worry way less about website SEO
1. Go to Google Maps, enter your business name, find your Map listing, click on Share, then click on Short link, and copy that link. Then you can use that link everywhere, even here on this forum. Also put that link on your website or embed your Map on your website, it's like a citation, a recommendation, to Google. If you have a Google Plus page, embed your Map there too.
2. Also have everyone you know go to Google Maps, enter your business name, and have them click on Save. This signals Google that your business is important to people. Just don't ask too many to do this all at once, ask maybe 2 or 3 people a week. Too much activity of this kind in too short of a timeframe doesn't look natural to Google.
3. Ask for reviews -- Google will greatly reward you for reviews, and people click more on listings with more reviews. Currently you need at least 5 reviews to get those valuable red stars to show in your listing.