Poor piggies...
Hmm. My kitten is the same way! :S A lot of people use wire shelving as tops. I don't use it personally (I use cubes), but I have heard great things about it. Somebody who uses it could tell you more about it.
As for your mom, tell her about all the health benefits of C&C cages. (Or at the
very least, a storebought cage, with an attached covered playpen.) Make sure to let her know that it will save on expensive vet bills in the future. That should at LEAST get you a pet store cage. No one here will recommend them, but its preferable to an aquarium. If she still won't change her mind, look into buying a C&C yourself.
The Coroplast shouldn't cost you more than $20. If you get scrap, (cosmetic flaws, misprinted, wrong size, overstock, etc) it should cost you $5-10, or be free. When you call (USE THE PHONE BOOK!), I personally say, "Hi! I'm making a guinea pig cage, and was wondering how much a piece of 4x8 Coroplast would cost?" If they don't know what Coroplast is/say they don't have it, explain that it's basically cardboard in plastic form. Other call it corrugated plastic. If a standard piece is too much, say "Hmmm. What about scrap? Do you have anything that was misprinted, cut wrong, or have cosmetic flaws?" Acceptable flaws are listed above. You don't want to get a piece that has a gaping hole in it!
Tell him the dimensions you want. (each grid is about 14 inches, so 14 inches x however many grids across you want it + 8 inches for the sides. Use this formula for both the length/ width of the Coroplast you want.) You could also duct tape 2 pieces together, which is what I did for my 1st cage.
2 boxes of WalMart cubes will be around $40 on the website. If your local store doesn't have them, go to walmart.com, and order them using Site-to-Store. They will bring it to the store for you to pick up for free. With 2 boxes, I made a 2x5, a 9 grid playpen, 2 hay racks, and had about 5-6 extra.
Cable ties (get at least 200~ you need about 2x as many as you think) will cost less than $5, if you get the little 4 inch ones.
All and all, the most it'll probably cost is $68, if you include gas money ($3, roughly)
The least: $48, also including gas money ($3, roughly)
Hope that helped! Personally message me if you have any more questions. Or quote me. I won't know that you asked me otherwise.