Let n,m∈N, and let Bn,m(RP2) be the set of (n+m)-braids of the projective plane whose associated permutation lies in the subgroup Sn×Sm of the symmetric group Sn+m. We study the splitting problem of the following generalisation of the Fadell–Neuwirth short exact sequence:1→Bm(RP2∖{x1,…,xn})→Bn,m(RP2)→q¯Bn(RP2)→1, where the map q¯ can be considered geometrically as the epimorphism that forgets the last m strands, as well as the existence of a section of the corresponding fibration q:Fn+m(RP2)/Sn×Sm→Fn(RP2)/Sn, where we denote by Fn(RP2) the nth ordered configuration space of the projective plane RP2.Our main results are the following: if n=1 the homomorphism q¯ and the corresponding fibration q admits no section, while if n=2, then q¯ and q admit a section. For n≥3, we show that if q¯ and q admit a section then m≡0,(n−1)2modn(n−1). Moreover, using geometric constructions, we show that the homomorphism q¯ and the fibration q admit a section for m=kn(2n−1)(2n−2), where k≥1, and for m=2n(n−1). In addition, we show that for m≥3, Bm(RP2∖{x1,…,xn}) is not residually nilpotent and for m≥5, it is not residually solvable.