Hi Jerry,
What you suggest is just about achievable, but it's not very predictable and I wouldn't recommend it.
Firstly, It's quite hard to get rich snippets for embedded YouTube videos - and secondly, if you want the YouTube video to rank again, this video will almost certainly outrank you unless you have an incredibly strong site - as such, you can end up driving traffic that you could have driven to your own site to YouTube - and from there it is extremely hard to drive referrals.
Secondly, While Google may choose to rank both pages, they often will just preference one of the videos - likely the YouTube.com version - which means your site won't rank at all.
Thirdly - The kind of videos that you should be aiming to get your site ranking for, normally conversion related videos - are not the type of content that typically provide any value on YouTube, so you should really consider who the target audience are for your content and whether they're people on your site or people finding the content via YouTube.
However, all this aside, If you really do want to get both a YouTube listing and your own site ranking - then I recommend showing Google that it's two different videos both relevant to the keyword - by self hosting the content on your own site (or using a paid third party platform) and submitting a video sitemap - then uploading the video to YouTube
However, I want to make absolutely clear that I don't really recommend the above solution from a strategic perspective, as the kind of content you should want your site to rank for is almost never also appropriate to put on YouTube.
Thanks,
Phil.