The Harvard lawsuit analysis implies that being a legacy is a strong hook. This analysis was done with dozens of regression controls, including controls for reader ratings of applicants. A legacy who has the same reader scores as a non-legacy in academic, EC, personal, athletic, LORs, alumni interview, … same REA/RD status, same …, was far more likely to be admitted.
In the study at http://public.econ.duke.edu/~psarcidi/legacyathlete.pdf , the author’s model estimates than a White non-legacy with the following chance of admission would see the following increase in chance of admission, if the only change in application was switching from non-legacy to being a single-parent legacy. All reader ratings and other aspects of the application remain the same.
If applicant had 1% chance of admit, increases to 8% chance
If applicant had 5% chance of admit, increases to 31% chance
If applicant had 10% chance of admit, increases to 49% chance
If applicant had 15% chance of admit, increases to 60% chance
The legacy admit rate by for applicants with 1-2 academic rating is based on the Harvard internal report at http://samv91khoyt2i553a2t1s05i-wpengine.netdna-ssl.com/wp-content/uploads/2018/06/Doc-421-112-May-1-2013-Memorandum.pdf . Legacies with a 1-2 academic rating (by far the most common rating for legacies is 2) had a 55% admit rate compared to a 15% admit rate for non-legacies with same academic rating.
While 55% admit rate is certainly high, it also implies that just being a legacy and having good stats (academic rating of 2 is highly correlated with stats) is not enough for admission. One also has to be quite successful in other aspects of the application and/or have additional hooks. Some legacies meet the other criteria. Some do not.
One also should note that admit rate has decreased since the time of the study., 'However, as discussed in the report at http://public.econ.duke.edu/~psarcidi/divergent.pdf , the legacy admit rate has remained largely unchanged over time. It’s the non-ALDC admit rate that has rapid decreases, not the hooked kids. This makes the ALDC hook increasingly powerful over time.
Regarding the OP’s kids, I have no idea what their chance of admission will be and certainly can not give a specific number like 50% or 60%. However, I think it is likely that the Harvard legacy status will make chances at Harvard better than other similarly selective colleges. For example, they might have a better chance at Harvard than many of the other highly selective colleges that have been mentioned in the thread. This is a moot point, if they don’t want to go to Harvard. One should apply to colleges based on desired personal criteria, not just because they may have a good hook.