Over the past few months, I've been running a campaign for my friends and we've currently arrived at one of my player's storybeats. I have planned for them to meet the one who orchestrated their family's deaths, which turned out to be a dragon that disguised itself as a human worker as revenge for her parents nearly killing them and stealing their hoard. With only one more session until this meeting, they and another player want to pitch to me an idea about how they want to intertwine their backstories by having the family of the other player be the ones who had the deaths planned. What should I do? Do I throw out my planned encounters and go with thier ideas or should I tell them that this feels too last minute? 

Too last minute for my taste - also, the other player is jumping onto the bandwagon of an other characters story arc? I'd let the player have their "solo in the spotlight" and give others their own - from their own backstory.

Alternatively, you could find a way to connect them AFTER you do the part you want to do. That way, it's more natural and thought out