TBH I don't see what else you can do.
Plan A - If your DP is honest and not after a visa and is truly kind and loves you, tell her you don't have the time to sort out a wedding, she can't work as an illegal or won't find it easy to find a job as an illegal, the only way is for her to go travelling again or back to Chile for now. A long distance LTR and time to do the research and gather information. You will also have time to find out more about each other.
Plan B - If she isn't honest and TBH from what you say here Plan B is already in action, she will move into your home in bits, stop studying and working, trap and leach off you until she decides to move on to sunnier pastures. Mouse problems are not a reason to stay at your house, they really aren't. Problem is you are in a pink bubble of loveliness you can't see it yet - when you do see it and you will eventually, the fall out and consequences will be far worse than the manipulation and bad feelings you will get when you ask her for the long distance relationship.
Plan C - She gets pregnant. Don't trust anyone telling you they make their own contraceptive arrangements, too many people men and women get caught out that way. A child doesn't shore up shaky foundations and the poor thing will only get caught in the middle.
Plan A is the only realistic option for you right now, it will be far worse if you go with B or C. As an intelligent, albeit lovesick man, wouldn't you rather have Plan A?
At some point soon you will have to bite that bullet. You could try to tell her you cannot marry right now because you have looked at all the options that you might help her with but there are no options that way right now. That you want to try the long distance LTR as it won't be difficult, you can make it work. She can't live with you right now because of her visa and that you want everything to be right and legal so you can have a proper adult relationship with her.
Don't let her move in, you need to protect your space, if she loves you she will respect that. If she doesn't she will start manipulating you even more. Unfortunately @murasaki has hit the nail on the head.
All the time you are with someone unsuitable, they are wasting your time, energy and emotions, when you come to realise this, anyone wasting your time will make you cross. From the way you are being played, she is taking up your time and headspace and it could be too late for a family by the time you realise that. Plenty of fish out in the Irish sea.