If the object were to wring the most ROI out of the second site, would you:
I can't say what I would do without a deep deep understanding of the site. I wrestle with these questions about pairs of sites that I have owned for ten years. A good decision has to consider many things, some of which are... A) content overlap, B) revenue source overlap, C) staff and financial resources available to work on another site, D) staff and financial resources required to improve the other site compared to the financial benefits expected, E) how close the competition is to kicking my primary site's ass, F) how close my primary site is to kicking competition's ass, G) how the profitability and fun elements of this job compare to the MANY others that are currently on backburners at my office, H) and, most important, how much mental energy I have for the fight.
A) Make the second site not much more than a link slave to the first, going through the trouble to keep everything separate, including owner, hosting, G/A, log-on IPs, so as not to devalue the links to 1st site, etc?
I would never take this choice. Just redirect the site instead of doing something that you think you gotta hide. This choice assumes that Google is a dumbass. They ain't.
B) Develop the second site and not worry about hiding that both are the same owner.
I have one domain that is a large site and competes with two smaller sites that I also own. The smaller sites have a niche specialty, so only a tiny fraction of the large site competes with them. All of these sites have the same whois, they are all in my webmaster console, they all have the same authorship style and are hosted at the same company in the same building. They all have absolutely unique content, very different, even if same subject. There are also some links between the sites, not a lot, no money anchor text, and the links are disclosed as being affiliated or both sites owned by same company. If you do all of the above, I don't think that you need to worry about Google getting angry about it. These sites have been doing this for ten years.
C) Develop the second site and still worry about it keeping it all hidden from Google.
I think that Google knows a lot about who owns websites. I might have private whois if I don't want people getting in touch, but I would not worry about Google knowing that same company owns them as long as you are not doing anything sneaky.
D) Buy the second site and forward the whole thing to site 1.
This is white hat in my opinion, but if both sites have similar link profiles at the domain level then you might not gain much from this method. Careful study is needed to decide if this is better than option B. How much work is needed to get the second site up to your standards and improve it to a point that it will become more competitive.
My pet peeve is folks who slam a fast/insufficient answer into an unanswered question, just to be the first. So, please don't.
How do you know their intent? Fast answers might not have that intent. Maybe my answer is Insufficient because I didn't give an answer that will satisfy a lot of people. Why? I didn't give an absolute answer because there isn't one without a really detailed study that I don't have time or any intentions to give. My pet peeve is when people want a $2000 answer for free in a forum and think that a $200 answer is crap because it didn't give an absolute answer.
I think that you either say "thanks" or nothing to anyone who gives you their time. An absolute answer to your question would require a content audit, a link audit, and a lot of information about your company and the industry just to get started. I think that it is a five digit question in many situations. And, you could pay five digits to two different people and get two very different answers. In that situation, you would need to decide who to believe. How are you going to do that?.
I am not providing a insufficient answer here because I am looking for paid work. I simply give two cent answers to people who might appreciate them. I took a chance on you.