Would it make a negative impact on my PhD application if they get to know that I am already enrolled in PhD and now applying for another program in their University?
Yes, you can apply, just as anyone else. But yes, it is possible that people in your current program would take it as a negative. And, yes again, that the other university or program might rank you a bit lower if you already have a "suitable" position in a doctoral program. But I doubt that the last would be a large factor in most cases.
But there are a lot of reasons to switch. Some of them are very important. If you have a serious need to switch, either for personal or academic reasons, don't hesitate to explore your options and follow up on good ones. This is especially true if you don't think you have a good path to success where you are now.
People understand that others change their minds and their directions. They understand the need to move locations and situations. They understand that some qualified students are in a bad situation.
Not really. There are people doing more than 2 degrees at the same time. That is relatively common for people that want to end up at the same time with extra certifications and there are universities that offer a discount on the second degree's payments. However, it is understood such is extremely demanding.
If what you are planning is a switch on PHD and you care what others may think, then there shouldn't be a problem either, but I advise you to say (and only if you are asked) exactly that, that you wish to pursue 2 PHD's simultaneously, and then, when you are on the other you can say that it was indeed too demanding and need to drop 1 to be able to finish the other. Otherwise, you are the paying client of the university (most PHD's around the world are paid for by the student and only so few are by scholarships), so if you want to switch then there shouldn't be a problem. And in the rare case its not a paid PHD (whihc can be the case for some european PHD's) , then just check your universities regulations to see if there is any type of penalty.