Back links to a new website

I have a website with PR2 and over thousand indexed pages. I created a new website and finished all the on-site SEO. My site was on Google's 4th page within a week for target keyword. I added a link of the new website to the old website. Now back link checkers show over 50 back links from old website (this is growing). I observed that Google started pushing my website on 5th and 6th page now.

Why is this? Shall I remove the link from old website? Does Google doubt that its link spamming?

it is just a google dance

Shall I be worried about it? Shall I remove the links and wait for a month or two?

Removing the links could take more than a month or two to see results, IF that were the reason to begin with.

If it's a dance you'll see it jumping up\down in positions from a page, all the way to different pages in the SERPs. It could just be the honey moon period after getting a new site indexed, where you see that you're ranking good\okay, and then drop many pages behind.

If you're hosting the domains from the same account, I wouldn't interlink them unless they're of the same niche, and even then I wouldn't leave an obvious foot print of that nature just in case.

Both are my own websites. Thus, it will take a minute to remove the link. My main question is: shall I remove the links? These are legal links though.

Sounds like you put the links in the footer on every page or something similar if you already have 50 backlinks from the old site to the new site. Take the link out of the footer and place it on the homepage only for a couple of 3 weeks. See what happens, return here and post results.

When I said "Removing the links could take more than a month or two to see results..." I didn't think you would be contacting a webmaster and requesting them to remove the links, I realized you were the sites' owner. I meant for Google to re-index, drop, and re-position when you removed the links yourself, if that was the cause in the first place.

Agreed, if it's a footer link, remove it anyways. The only reason you'd want to do this is if you're a web development company, or if you have authority and are linking to sister sites\partners. Footers aren't as effective as they once were due to abuse especially with regards to network schemes, but I'm not 100% certain this would be the cause for the lower rankings.

Yea, I would say that Google is just 'dancing'. Over time this will mellow out. It is just Google's systems determining trust. Just do not spam bad links, and you should be good!