In this article, we study the insertion pre-Lie algebra of rooted trees ( 𝒯 , ⊳ ) and we construct a pre-Lie structure on its doubling space ( V ˜ , ▸ ) . We prove that V ˜ is a left pre-Lie module on 𝒯 . Moreover, we describe the enveloping algebras of the two pre-Lie algebras denoted respectively by ( 𝒦 , ♦ , ϒ ) and ( 𝒲 , ⧫ , Θ ) and we show that ( 𝒲 , ⧫ , Θ ) is a module-bialgebra on ( 𝒦 , ♦ , ϒ ) . Finally, we find some relations between the enveloping algebras of the insertion and the grafting pre-lie algebras of rooted trees.