Why Hanuman Jayanti is celebrated twice every year

Hanuman Jayanti is celebrated on wrong date by many hindus, even by so-called pandits and saints.
Hanuman found Seetha in Lanka on early morning of a Tuesday. It was a Poornima (full moon day) with Moon in Chitra nakshatra (Chaitra Maasam according to lunar calender). On this day, Hanuman destroyed Asoka Vatika and killed multiple army men of Ravana, including Aksha Kumar. He even went on to burn half of Lanka on that day with his tail.
Hanuman destroys Asoka Vatika

This day is supposed to be celebrated as Hanumad Vijayam (Victory of Hanuman), but many ignorant people celebrate it as Hanuman Jayanti. It usually comes every year in April.
Hanuman was born on a Saturday, Sukla Dasami (10th lunar day after fullmoon) in Vaisakha Maasam (usually comes in late May every year), with Moon in Poorvabhadrapada nakshatra. This is actual Hanuman Jayanti according to Parasara Samhita, which is the only authentic complete book on Hanuman.
Hanuman was born to Anjana and Kesari, when Anjana was meditating for a child on Anjanadri hill (one of the 7 hills in Tirumala).
A Vanara leader killed 2 wild elephants named Sankha and Sabala to save Rishis from them in Prabhas Kshetra (Prabhas Patan). This place is in modern day Gujarat near Somnath Jyotirlinga Temple.
Rishis called him called Kesari (Lion) for his efforts.
Later Kesari also killed a rakshasa named Sambasadhana, which pleased devas.
They blessed him to get married with Anjana.

Kunjara raises Gautama-Ahalya daughter Anjana
This Anjana was born to Rishi Gautama and Ahalya, who were living at Janardhana Teertham (present day Kovvur in Andhra Pradesh).
Lord Rama travelled from Ayodhya to this place and killed demom Tataka and her son Subahu upon order of Brahmarshi Viswamitra, whose hermitage was also in nearby place.
Rama travel Ayodhya to Gautama Ashram
Brahma Puranam mentions the legend of Gautama and Ahalya.
He did farming in the surrounding regions to maintain his Ashramam. He used to generated lot of food grains, which made other brahmins jealous of him.
Gautama Maharishi once he accidentally kills a cow (tricked by others due to jealousy), grazing in his paddy field, by throwing a darbha (sharp, pointed grass). Gautama becomes upset with this incident and offers a great tapas for Lord Shiva in Brahmagiri mountains (Triambakam in Maharashtra).
Siva, pleased by his tapas, wipes away his sin and allows Ganga to flow in his farm to purify the place (originally called govuru, which means place formed by cow). The river thus originated is called “Godavari (Go-da-vari)” which means “originated due to killing a cow”. It is also called as “Gautami” in appreciation to the effort of the maharishi in bringing Godavari to earth.

Ahalya Ramayana
After Gautama cursed Ahalya, due to her liasion with Indra, he left her and also left their daughter Anjana with a Vanara named Kunjara, who was childless at that moment.
Ahalya is left alone and she stayed at Tougimi which is currently called Togummi (west godavari district, Andhra Pradesh). The place where the cow was died was chavugallu which is currently called Chagallu.
Ahalya stayed there until Brahmarshi Viswamitra brought Rama and Lakshmana to end her penance.

तस्य आतिथ्येन दुर्वृत्ते लोभ मोह विवर्जिता |
मत् सकाशे मुदा युक्ता स्वम् वपुः धारयिष्यसि || १-४८-३२

Translation : ‘On your welcoming of Rama, oh, ill-behaved woman, you will be divested of your greed and craze in which you lingered so far, and then you will assume your own body (self appearance) and then you can be in my proximity, rejoicingly‘. Thus, Sage Gautama cursed his wife Ahalya.

शापस्य अन्तम् उपागंय तेषाम् दर्शनम् आगता ||
राघवौ तु ततः तस्याः पादौ जगृहतुः मुदा | १-४९-१७

Translation : On reaching the end of curse she came into the view of Raghava-s (Rama and Lakshmana), and they too gladly touched her feet in reverence.

Daughter of Gautama and Ahalya, who was Anjana, raised by a vanara named Kunjara and his wife VindhyavaLi.
Infact, Anjana was an Apsara named ‘punjikasthala‘, who was cursed by a vanara hermit to be reborn as vanara woman and marry a vanara for making fun of his appearance.
Kesari killed Sambasadhana and met Anjana at same time. They both were attracted towards each other and Kesari asked Kunjara for his daughter’s hand.
Their son was Hanuman, who was born due to 2 boons.
Anjana tapasya on Anjanadri Tirumala
Lord Siva transfered his rudra-amsa (who was Aja-ekapada rudra in past) to Vayu Deva, who blessed Anjana .
Anjana son Hanuman

Hanuman Vijayam is the day in Chaitra Maasam, when he found Seetha in Lanka, destroyed Asoka Vatika, killed multiple armymen of Ravana.
Hanuman meeta seetha in Lanka

He was caught by Meghnadh, his tail was set on fire.
Hanuman tail burned

Hanuman used this to burn more than half of Lanka and return to kishkinda.
Hanuman burned Lanka
So Hanuman is grandson of Maharshi Gautama and Ahalya. His maternal grandmother was released of her severe penance by Lord Rama, who met Hanuman later in search of Seetha.

Hanuman born on Saturday and finding seetha on Tuesday, make these 2 weekdays important in his worship.