Why will the resulting force lines of two positive point charges be like this:
I would expect this:
First a comment about the following statements made by Kitchi and Wouter:
These statements are incorrect without qualification, and here are two reasons why:
If you want to make some statement about smoothness of electric field lines, (which you should try to avoid calling "lines of force"), then you really need to make some other qualifications that exclude such cases.
Second, these smoothness justifications are, to some extent, missing the forest for the trees so to speak. The crux of the issue is really addressed by richard. The way one obtains the field due to a charge distribution is by invoking the principle of superposition. This immediately rules out the second diagram you drew because if you simply add the fields of the two point charges vectorially, then you will see that the field lines look like you draw them in the first diagram.
The comment by @Kitchi basically says it all: lines of force should be continuous and differentiable and they should never intersect.
From a different, less mathematical point of view: the laws of physics are presumed to be deterministic (at least for electromagnetism, I imagine there are areas of study where this presumption is not made). So let's look at your picture and follow the path of a particle, say along the green line pointing to the upper left. After a while you get onto the orange line. Now, if you reverse time (a way to check for determinism), you follow the orange line down until you get to the splitting point. There, you have a problem, because you could go either way and you cannot deterministically determine (no pun intended) which way to go. So determinisim fails. This is another way to see why your picture cannot be the case. The first picture doesn't suffer from this problem.
In fact, I just realized you don't even have to reverse time: you can just consider an oppositely charged particle starting on the orange line. Then there is a huge issue when this particle reaches the splitting point. This problem does not occur in the first picture, where the force lines get infinitely close together after a while, but they never overlap.
It is easy to see that the second plot is wrong! For example consider the line at $45^o$ from the left charge. It says that the electric field direction is $45^o$. But you have to add electric field vectors of both charges at that point (at any point) which can not be in $45^o$ from the horizontal line!