I do not understand why this elementary question was closed. The official reason calls it a "homework-like question" and asks the poster to "show some effort".
One could argue about whether this is homework-like (though it seems clear to me that this is not an assigned problem, but rather something the poster stumbled upon while, quite admirably, attempting to invent and work out an illustrative example). But surely it shows an appropriate level of effort. The OP used the relativistic momentum formula (not the Newtonian formula as alleged in a comment) to compute momentum in an unambiguously defined frame before and after an explosion, came up with different numbers, is disturbed that momentum appears not to be conserved, and wants to know what's wrong here.
Given that the OP did all the relevant calculations, what additional effort was expected of him?