- There are 8.7 million species on the planet. That means at least 17 million animals needed to be housed. In addition, the Bible specifically mentions that Noah had to keep multiple of some animals for food or supplies. So, rough estimate, 20 million animals. That's far too many to survive on any ship or be fed and kept by a small extended family. The size in the Bible actually is not big enough. - The Bible clearly describes the flood as Earth-wide. That means that animals from all corners of the globe would have had to travel from their homes to the middle east. This means that creatures that normally live in humid or frozen climates would have had to had traveled and live in a middle eastern climate. - In addition, this mass migration would have had to had happened within a single lifetime for some animals, otherwise we would have to had left some remains or evidence of their mass migration (foot prints, remains, feces, etc). This journey would also require each animal to survive in pairs across vast distances in various climates without ever dying. The animals adapting for these climates is also not possible, given creationist views on evolution and the fact that it would have had to happen in such a short time frame. - A ship of that size would twist and buckle under it's own weight. Without modern technology, it would have been impossible for a wooden ship to not capsize under it's own weight at that size.
Seriously, though, I'd advise against trying to convince her otherwise. If she already buys the idea, it's based off of faith, and you aren't going to change that with facts. Just respectfully disagree with her and leave it at that. You aren't going to win her over by attacking her beliefs.