Why and how did Lord Shiva fall in love with Mohini?
"Any Shiva bhakt will be shocked if they read about this!"
One doesn't need to get shocked from this story. It can be interpreted in various ways:
i) Vaishnavite Interpretation:
This story shows even Shiva is bewildered by Maya of Vishnu. So, Vishnu is Supreme.
ii) Shaivite Interpretation:
This story shows Vishnu is Prakriti tatwa (feminine) and Shiva being Purusha is attracted to Prakriti. So, as Shiva is Purush as clearly seen from this story, Shiva is Supreme.
iii) General Interpretation:
This is Just Leela of God and done for the specific purpose.
Coming to your second question:
"Also, he is already married to Parvati, who is Tripura Sundari, the most beautiful woman in the three worlds?"
If you closely look at the story of Brahmanda Purana you will find that Vishnu is changed into the form of Tripura Sundari or Uma herself. It looks like 1.5 of Rudra Hridaya Upanishad which states "She who is Uma, she herself is in the form of Vishnu”. Here are some relevant portions from Brahmanda Purana.
"Meanwhile, Vishnu began to meditate on Sri Lalita Mahatripurasundari, who was his very own Self. By completely identifying himself with Maheshwari, Vishnu manifested himself in her form. She looked as if she were the very personification of the sentiment of erotica. Decorated with all kinds of ornaments, she appeared on the battlefield and brought the battle to a sudden halt. Enchanting the demons with a smile. The parting of her hair was decorated with a vermilion mark. Her crown was decorated with the half-moon. Her eyes were filled with intoxication. Filled with desire, Shiva followed her and taken her into his embrace, as a result of which he ejaculated his semen. Immediately, an immensely powerful god named ‘Maha-Shaasta’, who was capable of destroying crores of demons, originated from Shiva’s semen". [Brahmanda Purana Lalitopakhyana chapter 2]
So, as evident from the above description, Mohini form of Vishnu is just, Vishnu being converted in the form of Tripura Sundari. That's why Mahadeva is attracted to her.
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