My theory about how Rin got in the tree of ages goes two ways.
1. Kirinmaru freed Root Head and then Root head held her hostage in the tree.
2. Rin was poisoned after giving birth to the twins, taken and put inside the tree of ages to recover( Without anyone knowing that root head was corrupting it) and Treeko told Sesshomaru that Rin's recovery comes with a price, the price that one of his daughters memories and dreams would be taken.
The only thing that we can gather without speculation is that she had just given birth to the twins. She's wearing what feudal era women wore when giving birth.
I don't trust Treeko
I think the tree is still salty that Inuyasha got pinned to it for 50 years.