Speaking as a parent myself: You are an adult. You are not only allowed, but supposed to live your own life now. The clock is ticking on you living with your parents; when there is a good occasion to leave your home, then you can and should do so.
That has nothing to do with whether you have a good relationship with your parents or not, or with your potential wife.
So, by all means, leave your home and do what your heart tells you to. It is your decision, not your parents'; and the question whether your future wife is the correct one will not be resolved by your parents anyways.
Parents can't stand your wife
As tough as it sounds, that is their problem, not yours. It will only become your problem if their dislike transfers over to you, and they do not want to see you anymore, as well, if you marry your wife.
But: frankly, if your parents are so petty that they want to "divorce" you from the family because you love someone else, then you should probably think long and hard what is more important to you - your future or your past. Yes, it may be hard on them, and reciprocally on you, but nothing will change that anyways. The damage is already done by your mother pulling the rug out from under you. If you leave your future wife now, you won't exactly have a very fun future with your mother, anyways, will you?
If they keep the door open for you, but do are not friendly to your wife afterwards, then you will likely need to resign yourself to visiting your parents without your wife, in the future; or you might find a way to visit your home country together with your wife, stay with friends, and visit your parents for a day or two on your own. But that is nothing special, and many families have the same issue of people not liking each other that much (without going to outright warfare). You will survive, it will not be that much of a problem.
Of course, you will want to not be dependent from your parents after moving out. I.e., make it a clean separation. You are now living on your own, together with your wife, period. You will not be asking them to send a monthly cheque or something like that.
How to go about it
You should be very aware that your parents don't have any legal or moral say in this (neither your choice of a partner, nor when you leave their home, or where you go to live), in our western culture. This means: you do the decision making, and you stand by it. You do not fight with your parents about it. You tell them how it is, and they accept it, or not, but you do not burden them with asking them what to do, or even putting up a facade where it seems like they have a say in the matter. It is not an issue where you need to achieve consensus.
You will still stay open to them, even if they (try to) make it hard for you. If they start fighting, that means that it is hard for them; they "lose" their child, their live will get a lot quieter, they have to give up someone who they cared for their whole live. You can help them get over it by making every humanly possible attempt to stay friendly and open with them, but you still have to do your choice and tell them in very clear terms.
How do I tell my parents that I want to marry her and move over there in a few years?
I understand that as "I want to marry her in a few years and then move over there". Then there is no reason whatsoever to tell them now, since things could change between you and your prospective wife in the next years, anyways. That would, after your history, just be an empty threat right now, as petty as your mother making their dislike of your wife so clear.
I'm afraid they will start yelling at me,
Work on yourself; this should not be a threat to you. You are an adult, you will survive shouting. Take it as a learning possibility; try to react without shouting back, staying calm and composed. And, as said, if you already know that a topic will make them start to shout, then don't bring it up, it's not their business.
disallow me to do that
They cannot. They can withdraw things like their "love" (which there seems to be not much around of, anyways), their heritage, if there is any, but any of this is survivable for you, and unless we're talking billions of € here you should probably make your own living before this is an issue, anyways. ;)
or that it will make the relationship with my parents even worse than it already is.
That could well happen, but that is the way things go. If I read between your lines correctly, this would happen with any other life-changing event in your family as well. You will have to move on. I do not see anyway to make your mother like your wife with these kinds of regular visits. Maybe they will grow closer after you get children, maybe not, but that's after the fact.
I don't know what to do or how to tell them that I even asked for her dad's blessing.
It is not their business, you do not need, and probably should not tell them.
I'm afraid I will mess up things and make things only worse when I tell them.
Do I even need to tell them my plan of proposing at all?
Not at all.
I don't know what to do in this situation and it's really stressing me out. Any help is appreciated.
Get your thought processes in order: your parents were very important to you for your first 18 years. At 20, you are in a transition phase. Somewhere in your 20's you will leave your parents. Start now by separating their lives and concerns from yours. You are allowed to have private matters that you don't share with them. Their emotions are not yours. Yours are not theirs. Their problems are not necessarily yours, and so on.
It is not quite easy to wrap your mind around this mindset, but it is possible. It is time to increase your separation with your parents; this will make it easier and/or (if it takes a few years until you marry, anyway) a non-issue.
If you are able to live somewhere else (still in your country, before moving to the U.S.), it might just be a good way to practice that before you do the big move. Then you will also have a natural separation, and things will cool down.