If the flour you are using is one of the more high-gluten flours, which binds together better, then you can just leave out the eggs without needing any substitute at all! (any wheat flour should hold itself together just fine, or if you can actually get powdered gluten on its own then you could add it to any other type of flour and it would work, too)
:)
I pretty much just threw in a couple of eggs because the flours I was using weren't wheat flours and I knew they would fall apart without some help, and I didn't want to use that chewy, gluey-texture from working up the starches too much.
If you were doing it in muffin cups or small loaf pans or something else confined, you also wouldn't need it to hold itself together as much, and could leave it out without worrying about flours.
Maybe you can make a deal with your mom where every time you cook with her, you cook one traditional dish and one thing you're interested in trying? Then you can slowly be expanding her repertoire at the same time you are learning how to cook, and if you happen to be practicing on dishes that you aren't so very fond of....
well....
when you're first starting, the first dishes don't tend to turn out anyhow! "Small loss", as they say. Since you didn't like them to begin with it won't matter if they don't turn out perfectly while you're still learning
although, she wants me to learn our traditional cooking, of which I only enjoy certain dishes.
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if I asked her to do this with me, though, she'd be pretty happy I think. Because she'd get me to cook the things she wants as well. So far it's been like, with some scolding, I'll watch her while she cooks. And with more scolding, I'll chip in when she wants me to. 
imagine, I didn't even know that you had to wait for the cake to cool before cutting it! We were all enthusiastic about eating cake warm from the oven, and ended up eating very crumbly, falling-apart slices 
