Reidy has given some major salient reasons for deciding to go.
I only have to add the following:
Any consideration of “should” is to be viewed from the woman’s rational “self-interest”. One cannot forget that starting point whenever determining a moral/ethical question.
Some facts which play into this:
A. A dead person has no existence and no value, but a living person’s memories, feelings, and thoughts of a dead person do exist and can have value (or disvalue), often profoundly affecting that person’s experiences and actions going forward.
B. Children, common friends, in-laws, and current spouse, who are all alive, are a value to a person, and that includes their well-being, and their relationship with the person.
The woman should consider what the likely factual consequences of her actions would be were she to choose to abstain from going as against were she to choose to go, and to evaluate them against her hierarchy of values.
A2: Without resorting to psychoanalysis, a funeral service can provide time and context, an event with people and stories etc. to provide reflection and closure on the loss, i.e. the passing of the woman from a world in which the deceased was alive into a world they are absent from can be quite profound. There may be very real personal psychological reasons why the woman herself, for her own psychological well being, should go [possibly some reasons not to go]. It must be evaluated in her context.
B2: Since others are a value to her, [and if you are a parent you will understand how precious children are (no matter what age) to a parent] in order to serve herself she cant ignore the effect that her actions have on them. Reidy has outlined why this is important. To a lesser degree this applies to considerations in regard to common friends, and in-laws.
The thoughts and feelings of the new spouse and the ongoing relationship are also important. Once and if the woman decides to go, she should have a conversation with her spouse explaining WHY it makes sense for her to go, personally, and in support of other people and her relationships with them, which she values highly. If she has a good relationship with the new spouse and he is rational and values HER, he will understand and be comfortable with it.
IF he is NOT rational, DOES NOT value her, or if their relationship is rocky to the point he does not or is unwilling to understand, then the context changes drastically, and the moral questions open up to much broader than simply deciding whether or not to attend a funeral…to a whole range of options including, taking a hard look at who she is with and whether they should stay together.