Is it 100% permissible lechatchila to say Havdala before arvit on Motzae Shabbat or Yom Tov, if one is going to pray arvit late, for example, if one wants to go to a distant synagogue from his house?
What are the sources for the answer? Thanks
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Yes it appears to be permitted
Shulchan Aruch Harav (293:1) writes
as soon as three stars can be seen next to each other, it is permitted to recite Havdalah and perform labors [forbidden on Shabbos] even though one has yet to recite the Evening Service
but see here that
every meticulous person is to delay doing any [Biblical] Melacha until the congregation has recited the Seder Kedusha after Maariv
(meaning you should wait a few minutes before doing melacha)
and here that
some Poskim [Tehila Ledavid] however rule it is always proper to first Daven Maariv and then do Havdala in order to follow the set order that the Sages established.
dinonline writes (the question is asked on sha’as hadchak a time of need, but the end of the answer applies to all situations:
The enactment of havdalah includes two parts: One havdalah in davening and the other on a cup of wine.
There is no specific order for the two parts, the Gemara mentioning that somebody who made havdalah in davening must also make havdalah on the wine (because this was the original enactment), and somebody who made havdalah on wine must also add the havdalah insert in davening (because this is part of the motzaei shabbos prayer).
Therefore, it is fine, certainly where there is a need, to make havdalah before davening Maariv.
R Yosef Weitzen writes here
You can make Havdalah before Ma'ariv in such a situation [guests need to leave immediately]. You are obliged to drink the wine and you do not have to repeat Havdalah after Ma'ariv.
See also here
I personally think it is especially fine if it allows you to pray with a minyan later on vs. pray on your own at the end of shabbat/yom tov.