There is nothing to unite in Hindi-Urdu. Hindi is a post 1947 creation, an artificial creation of post independence India, by removing the Persian/Arabic loanwords from Urdu. Hindi has no independent history for itself from Urdu. Urdu evolved in the early 1200s from the Delhi Sultanate, & then rose to other centers in Lucknow, Hyderabad & Lahore etc. These 3 centers played an important role in the development of Urdu over the years. Before the invasion, the Awadhi, Braj dialects, Khari Boli were spoken in the Indian subcontinent.
When the invaders invaded India, their Turkic/Mongol lingual roots, along with the Persian dialect (they came through Persia to the Indian subcontinent), along with their Muslim Arabic roots amalgamated with the local Awadhi, Braj dialects, Khari Boli; & gave birth to Urdu. Which is why Urdu has a much larger influence from 'local dialects', but not as much from Persian & Arabic. As these invaders interacted with the locals there (who spoke Khari Boli, Awadhi & Braj dialects), & then the language evolved, with the "local influence of India more prominent than the Mongol/Turkic/Persian/Arabic influences of the invaders"; which resulted in the evolution of Urdu in the 1200s.
Urdu was known as Hindvi by Khusro in the 1300s, it was also given other names such as Delhvi (Delhi), Dakhani (Hyderabad), Rekhta (Lucknow) etc. Urdu evolved fast, & displaced Persian as the language of the courts. The language called 'Hindvi' by Khusro in the 1300s resembles the Urdu of today, just go back & read Khusro's poetry as well as the poets from his time, & before him. It had a lot of Persian/Arabic loanwords with a lot of Sanskrit based terms. Sanskritized Devanagari was used for religious Hindu scripts prior to 1867. In 1867, the Hindi-Urdu controversy arose, where the Hindus in Bihar & other states converted the Nastaliq text of Urdu, & called it Hindi.
Post 1947 independence, that was when Hindi was manufactured in India, by removing all the Arabic & Persian loanwords, & replaced them with Sanskrit ones. Hindi is an artificial invention post 1947 in India, there was no language called Hindi before that in India. It was Urdu, but in 1867, was converted into from Nastaliq to Sanskrit Devanagari text, & called Hindi. But it was still Urdu.