Relationship between Buddhism, Hinduism and Yoga?
Hinduism &amp; Yoga aren't 2 different things. They are the same. 
Yoga is one of the 6 main Darshanas of Hinduism. I.e it provides it's own path for liberation. Other Darshanas(Advaita, etc) too use Yoga as a valid means but not the only valid means. 

Can't really say Buddhism is modern. It evolved along with Yoga both of which can be traced to around 4th century BCE. 

Both Hindu Darshanas &amp; Buddhism evolved influencing each other. For example Advaita borrowed some of it's elements from Nagarjuna. Tibetan Buddhism incorporated Tantra which is considered 'Hindu'. 

Tibetan Buddhism has it's own version of Yoga called Trul khor.

Hence to answer your question, they all belong to the same family, the Dharmic family and have influenced each other.