I am merging duplicate people.
The spouse and a child also need to be merged with duplicate records.
What is best practice when this is the case?
Best practice is whatever will allow you to keep track of who's who and what's what. The change logs of the family members will look very strange and confusing, no matter what you do, so just make sure to always write a detailed reason statement that includes both of the affected IDs.
Am I able to merge the wife and child after I merge the father, using the IDs?
Yes. Each member of the connected family can/should be merged, one at a time.
To answer your title question, of what happens to the family members in a merge, I kept track of the change log entries as I did a pair of merges (mother and father).
Family 1: FatherA, MotherA, DaughterA. Both FatherA and MotherA have parents and siblings in the Family Members section.
Family 2: FatherB, MotherB, DaughterB. No other relationships.
Step 1: merge FatherA with FatherB (FatherA as the survivor). Make sure to carry over/transfer MotherB and DaughterB during the merge. Enter detailed reason (RS1).
Results of step 1: FatherA now has two wives: MotherA, with child DaughterA, and MotherB with child DaughterB. MotherA has parents and siblings, MotherB does not.
FatherA's changelog has one new item, a merge, with reason RS1.
MotherA has no new entries in her changelog. DaughterA and the parents of FatherA and MotherA likewise have no new changes.
MotherB has four new entries in her changelog, all with the same reason statement (RS1): Relationship Added (Husband FatherA), Relationship Added (Child Added: DaughterB with parents FatherA and MotherB), Relationship Deleted (Husband FatherB), and Relationship Deleted (Child Deleted: DaughterB with parents FatherB and MotherB).
DaughterB has three new entries in her changelog, all with RS1 for the reason: Relationship Added (Father Added: FatherA), Relationship Added (Mother Added: MotherB), and Relationship Deleted (Child Deleted: DaughterB from parents FatherB and MotherB).
Step 2: merge MotherA and MotherB (MotherA as the survivor). Again, make sure DaughterB is transferred, and write a detailed reason (RS2).
Result of step 2: FatherA now has one wife, MotherA, and two daughters, DaughterA and DaughterB. Both husband and wife now have parents and siblings in the Family Members section.
MotherA has one new changelog entry, a merge, with reason RS2.
FatherA has three new entries, all with RS2: Relationship Added (Child Added: DaughterB with parents FatherA and MotherA), Relationship Deleted (Husband FatherA and Wife MotherB), and Relationship Deleted (Child Deleted: DaughterB with parents FatherA and MotherB).
DaughterA still has no new changes (since her parents are the survivors). Likewise no new changes on the parents of FatherA and MotherA.
DaughterB has three new entries: Relationship Added (Father Added: FatherA), Relationship Added (Mother Added: MotherA), and Relationship Deleted (Child Deleted: DaughterB from parents FatherA and MotherB).
As you can see, the results in the Family Members section are fairly straightforward, as are the changelogs of the profiles being merged. The changelogs of the spouses and of the children attached to parents who are merged away ...are a bit complicated and scary-looking. (Something about the word "deleted".)
I do wish those individual changes to relationships could be presented in the change logs under a single item, labeled something like "merge of [relationship]". (Basically, anything with a single reason statement should be listed in all changelogs as a single action/activity. If that single action is composed of multiple parts, there can be some sort of "expand" link to show them.)
I find it helpful to merge the children first, then merge the parent(s). That said, it works either way and sometimes (often inadvertently) I merge the parents first. I don't always find all the duplicate children until merging the parents is in progress.
I almost never encounter duplicate children, so I have no experience with that angle. (The closest I get is finding a mother's own baptism while merging all of her duplicates that are based on her children's baptisms. That's not really merging a duplicate child, though, because only one of them has parents.)
I'm curious to know what difference it makes in your experience whether you merge the children first or the parents first? Does it make the process smoother? quicker? easier? Does it improve the resulting change log?
(I can't imagine it would change whether or not you decide to go forward with the merge; that's an issue to resolve separate from actually doing the merge.)
As an enhancement suggestion, I envision the ability to merge multiple family members as a group. I imagine an interface similar to the source linker, in which matching individuals are aligned or connected and marked as matching duplicates.
I merge the parents first because it makes keeping track of any duplicated children easier. They will show in the list of children of the newly-merged parents. 2 sons named David Ephraim Elder, both of whom lived to adulthood, show as obvious duplicates.
I'm curious to know what difference it makes in your experience whether you merge the children first or the parents first?
Merging the children first is an easy way to remove those pesky duplicate links to just one parent, and also to find and remove links to wrong sets of parents.
I do one child, then in their parental list (or lists) merge any duplicated siblings. Then I merge the parents.