The structure of the isodoublet hypernuclei, 10Λ B and 10Λ Be within the framework of an α + α + Λ + N four-body cluster model is studied. Interactions between the constituent subunits are determined to reproduce reasonably well the observed low-energy properties of the αα, αN, αΛ, ααΛ, and ααN subsystems. Furthermore, the two-body ΛN interaction is adjusted to reproduce the 0+-1+ splitting of 4ΛH. The ? binding energies of 10Λ B and 10Λ Be are 8.76 MeV and 8.94 MeV, respectively. The energy splitting of the 1-2- levels in 10Λ B is 0.08 MeV, which does not contradict the experimental report in BNL-E930. An even-state ΛN charge symmetry breaking (CSB) interaction determined from the A = 4 systems works repulsively by +0.1 MeV (attractively by -0.1 MeV) in 10Λ Be (10Λ B). We discuss a possibility that an odd-state CSB interaction improves the fitting to the experimental data of A = 10 double Λ hypernuclei.