Is it obligatory for her to enroll in an institute to learn Tajweed, which would require her to travel 10 km, or is it sufficient for her to rely on self-learning through CDs and memorization?

If studying at the institute is free from prohibited mixing and seclusion, then it is preferable to distance learning, due to the direct reception of recitation, the correction of reading, the regularity of study, and the benefit of discussion and inquiries. However, if going to the institute entails a forbidden شرعي (legal/religious) consequence, then one should limit oneself to learning through a device or searching for learning methods free from such prohibitions, as mastering the Qur’an is emphasized for those who are able to do so.