Split paper into two, one was accepted, is it fine to negotiate the rejected paper to be accepted?

Now, can I write to the conference and tell them to review the paper or argue with them that the paper could be accepted based on points made by the two reviewers?

You can try, but what do you have to tell them that they do not already know? They have already read the reviews, thought about them and reached a decision. Unless you can think of a compelling argument that invalidates or rebuts the criticism of the unfavorable review, your chances of success are essentially zero.

In my field, that would almost certainly not work. If anything, it will send the signal to the program chairs that you're very inexperienced with how the conference process works.

Conferences have a certain timeframe for reviewing, followed by a discussion period and a decision about each paper. It's practically unheard of that a paper that was rejected in this stage still got accepted due to some authors appealing.

(CS perspective / I was conference chair and program committee chair several times):

You made your choice and now you have to live with it. You have until submission of the final version to make sure that the paper is readable and self-contained. Since the accepted paper was reviewed independently from your other submission, that should be quite possible. You might disagree, but the reviewers thought it could live on its own.

You can publish your other paper on a preview server or as a technical report at your university / department / personal web-page. Pre-publishing it there should not hurt its chances of being accepted elsewhere. This way, you can cite and refer to it.

You can either submit the other half to a different conference or you can work both of them together and submit to a journal. This is standard practice in CS.

If you were to try to negotiate with me, I would be quite annoyed, though of course trying to be polite.