Here are the six concepts I'd look at. First, keep in mind that both United and AA offer one-way award travel at half the cost of a RT award--Delta charges the same amount for a RT or one-way ticket. Given the slow rate at which you will accumulate miles, you may find it best to accumulate on both AA and UA, assuming those two airlines will fly the route you want, so that the small totals you accumulate may buy you one-way on one airline and one-way on another coming back (I'm assuming for the moment you and your mom will want to fly together!). There are not many 500-1000 mile offers for free, like the MyPoints deal, but you'll find that some of these tend to repeat themselves across airlines (Netflix has a deal for bonus miles for signing up for a one-month trial with UA, DL, and AA).
Second, I'm assuming you still have the Citi Mastercard you took earlier. Although Citi's rate of earning AA miles is pitiful, if this is going to be the only credit card arrow in your quiver for the time being, use it to the fullest. As much as you can, run every piece of daily spending through it. Gas, groceries, cell phone bill, insurance payments (especially if no "convenience" fee is charged)--all of it has to go through your card. Scrutinize your budget, be aware of every penny you spend, and realize you need to pay any and all bills, expenses, and no-thinking spending (Coffee at Starbucks? On the card. Buying a magazine? On the card. Putting tires on your car? On the card.) with your card, if possible.
Third, surveys and sites like emiles and erewards, similar to MyPoints, will also offer some small, incremental earnings that might turn into a decent pile in two years. I know UA participates; I'm not so sure AA does. The surveys can be time consuming, but if you have time more than money, this is a no-cost way of getting miles.
Fourth, make sure you maximize your dining program participation. From your comments, I'm assuming you're a member of the AAdvantage dining program. UA has a similar program, and I believe is still running a 1000-miles signup bonus. I understand you're frugal, but if you are going to get to your goal, you'll have to take advantage of spending you already do. So, no dining out should occur that doesn't occur at a program restaurant. If that means you can't go to your old favorite restaurants, find new favorite restaurants within the program. Make sure you're signed up for their emails (takes you from 1 mile per dollar spent to 3) and try to get to 12 dines per year (takes you from 3 to 5). To get to 12 quickly, find the cheapest place in your dining programs near you and hit them for a coffee 12 times so that you can qualify for the highest earning ratio. Assuming you have trustworthy friends, be their banker when you go to a program restaurant--if they pay you cash and you pay the entire bill by credit card, you can get a pop of 500-1000 miles in one sitting while maybe spending $30-40 of your own money.
Fifth, look at the shopping sites and promos for good cost-efficient methods of earning miles. See the Netflix offer above. Take the offer, earn the miles, cancel after a month. The AAdvantage shopping mall offers 1761 miles for a 90-day subscription to the NYTimes. You don't have to order delivery every day; take the Sunday Times at $3.90/week and cancel after 90 days. And then, 90-100 days after that, do it again, as allowed by the T&Cs. And, if your mom likes the Sunday Times or Netflix, do the same thing for her. There are other similar offers so spend some time looking for methods of earning that will get you 1000 or so at a time. Get familiar with the offers. That way you'll be prepared to take advantage of a future situation that might earn miles (looking to change cellphone plans in six months? AT&T will give you 1258 miles for a new phone and two-year plan).
Sixth (and I know somewhat at odds with your current desires), consider a strategic application for a credit card or two in the winter of 2013-14, especially if UA or AA have a pending offer for a first-purchase bonus, even if it's smaller than a bonus connected with a significant spending requirement. Neither have that card in the stable right now, but last May, I took a Chase Continental One Pass card that gave me 50K miles after the first purchase. Even if you can get a card for 25K, that one application might prove to be the boost that puts your pot of miles over the top.
Fortunately, you have a narrowly defined goal and several years to achieve it. Use the resources you've found here at FT to stay on top of deals--the MilesBuzz forum is great for this, but I'd also take a quick look at the UA and AA forums as well as the credit card and S.P.A.M. forums here to see if there are any changes in offers. Keep in mind, however, that you probably don't have two years to build your miles, but more like 18 months. Award availability can be tough as you get closer to the dates of your trip so it's best to have the necessary mileage in hand well before the dates of your trip or, at least, to be flexible about when you might travel. That's another supporting reason for taking a credit card towards the end of this period--graduation will be in sight and you'll perhaps be able to overcome your understandable reluctance to take out cards, given that you should start earning money as you move from school to internships/residency.
Good luck!