First, so sorry this is happening to you and your family. Second, I want to say you are obviously a generous, loving, and mature person who values her family and loved ones above herself. You found out you could no longer have the "fancy" wedding your parents had planned, but you are more concerned about their well-being than your own wedding, and you are even trying to help your parents out. I see so many selfish brides out there who freak out about the tiniest things, and would rather see their parents go into huge amounts of debt just to get what they want. I think you are awesome.
As far as venues, i am not familiar with your area so I can’t reccommend anything specific, but the suggestions here are good. It is more work, but if you think creatively you can probably come up with something. Ask everyone you know if they have any ideas, no matter how strange.
Parks are good. Make sure you are allowed to have alcohol before you roll out the kegs.
You said you don’t have a house, but if you rent an apartment, some apartment complexes have a pool/clubhouse/courtyard area that residents can often use for parties. I have actually been to two wedding receptions like these and they were great. One wedding had the ceremony on the beach, which was free and simple and beautiful (they made an aisle with shepard hooks stuck in the sand and flowers on them) and the reception-party was essentially the keg BBQ thing and they had it at the pool of their apartment, which had a central courtyard area, and the guests just used the couple’s apartment for the kitchen and bathroom. The downside to this is that you probably have to check with the property owners to make sure it is OK for fire-codes, alcohol, etc, and you can’t keep other people out if it is a public space. Do any of your friends or family members have someplace like this?
Do you know anyone (or even a friend of a friend) who has a business, like a restaurant, bar, store, art studio, farm? People are often really willing to help, even if they don’t know you directly. You really just need a space with bathrooms nearby.
In my area there are a lot of community centers that allow people to rent rooms for events, not always glamourous, but they can be cheap. Check with VFW halls, American Legion, etc. Do you have any friends or family members that belong to any clubs?
If you look into renting a vacation house, make sure the contract doesn’t explicitly forbid having a party there (but if it doesn’t, maybe don’t mention that is your intention so they don’t add it to the contract).
Sometimes unexpected places can be rented cheaply. For example, I found out that a local community art center near my house can be rented out for private parties for only a few $100, and that included a nice garden area. If you see a spot you like, it doesn’t hurt to ask people if you can use it, especially after you tell them your situation.
I hope you find something that will work for you, and if you can, please let us know how things work out.