The aim of this work is to further develop the calculus of (internal) relations for a regular \( \mathsf{Ord} \)-category \( \mathbb{C} \). To capture the enriched features of a regular \( \mathsf{Ord} \)-category and obtain a good calculus, the relations we work with are precisely the ideals in \( \mathbb{C} \). We then focus on an enriched version of the 1-dimensional algebraic 2-permutable (also called Mal'tsev) property and its well-known equivalent characterisations expressed through properties on ordinary relations. We introduce the notion of \( \mathsf{Ord} \)-Mal'tsev category and show that these may be characterised through enriched versions of the above mentioned properties adapted to ideals. Any \( \mathsf{Ord} \)-enrichment of a 1-dimensional Mal'tsev category is necessarily an \( \mathsf{Ord} \)-Mal'tsev category. We also give some examples of categories which are not Mal'tsev categories, but are \( \mathsf{Ord} \)-Mal'tsev categories.