If you are asking “can I negotiate an extra 2 or 3K in aid from Northwestern” then sure- there is no downside in trying once you have an offer from a peer school. (I don’t think Trinity is going to do it for them…) If you are asking “will Northwestern match Princeton’s aid” then I’m going to advise you “not very likely”. Princeton has the most generous aid in the country-- according to folks who have compared P’s offer to a bunch of other colleges. Northwestern does not try to math P- and in fact- most colleges do not, except for Harvard or Yale.
So go ahead and try- but honestly- the sooner you fall in love with an affordable option, the sooner you’ll be able to move on emotionally from Northwestern.
Does your dad realize what your financial situation is right now?