The subjunctive clause
It is expected that I comfort the bereaved families
correctly uses the subjunctive form of "to comfort". Adding "should" is redundant ("should" is already implied by "it is expected"). It's too verbose and a bit awkward.
Side note: the trailing clause could be stated better. For example,
It is expected that I comfort the bereaved families, that I be present during this trying time.
Notice that the second clause (after the comma) uses the subjunctive again ("be") since the two "that I..." phrases are interchangeable. The second "that I" is optional but (in my opinion) preferred.