I am going through a divorce, if a child dies are both parties entitled to split the funeral cost 50/50?

There is no 50/50 rule. However the parties work it out is up to them. If you went to court on this, asking a Family Division judge to rule on which parent gets stuck with the kid's funeral bill, the judge would probably make the person who earns the most pay for the lion's share of it, or in proportion to respective income of each party.