Actually, Prince Victor Napoléon was more of a conservative with maybe corpatist views similar to the ones expressed in the manifesto of Prince Eugene (Napoléon IV).
Having read the biography of his father by Michele Battesti, I can say that he and his father had broken off and were political rivals.
In the aftermath of Napoleon III's exile and death, his cousin Prince Napoleon, and Empress Eugénie seconded by Rouher, both struggled to gain control of the Bonapartist party in France, Prince Napoleon even standing against an official but conservative Bonapartist candidate. Under the influence of the conservative Bonapartists, the Imperial prince developped a distrust towards the cousin of his father which was still the next in the line of succession and decided to use a proviso of the Senatus-Consultus of July 1856 ( act which settled the modalities of imperial succession and regency), a proviso which allows the Emperor to adopt an heir (akin to the former Roman practice) among the collateral houses of the family; Napoleon III had envisioned it so he could bypass his mistrusted cousin but never had to use it as Eugénie gave birth to a boy. It was thus that Napoleon Victor became the heir. However, Prince Napoleon never recognized the move and styled himself as Napoleon V after Prince Eugene's death ( for some Victor was thus Napoleon VI and not V).
Not improving the situation was the notorious womanizer behaviour of Prince Napoleon that his very catholic and pious wife (an irony when we consider that the Prince was a declared agnostic ), Princess Clothilde of Savoy, only accepted to endure it while the Empire was still standing. It was not long after the exile began that their marriage fell apart, ending with Clothilde leaving with their daughter for Italy.
The opposition between Prince Napoleon and his son took during the 1880's more the form of an ideological divide than a mere dynastic rivalry. Whereas Victor remained the head of the monarchist face of the Bonapartist, Prince Napoleon abandonned the idea of a new imperial restoration in favour of a Republican Bonapartism, a doctrine based around the idea of a presidential republic and direct elections; this latter trend, although marginalized by Victor's followers, ultimately triumphed as the current 5th Republic founded by de Gaulle is roughly organized on these same ideas and became with Prince Louis (who took part in the Resistance during WWII) the official ideological line of the Bonapartist party.
Prince Napoleon's support of ''Republican'' Bonapartism may seem in contradiction with the dynastic claim for he actually gave up the throne, but such perspective would forget an essential element of Prince Napoleon psyche. The character was still very impregnated with the Corsican roots of the family and conceived the Bonapartes more as a ''family'' than a ''dynasty''. The dynastic struggle was actually in his eyes a matter about the traditional role of ''patriarch'' he felt that was legitimately belonging to him .