Is a woman forbidden from speaking to her relatives that are non-mahaarim (i.e. lawful for her to marry)?
Speaking to non-mahaarim relatives is inappropriate. If she calls him due to a necessity and there is no fitnah upon her or upon him; this is something else.
If it is due to a necessity and without fitnah (temptation to commit sin) and seclusion then this is not a problem. If It is unnecessary then it is inappropriate.
The two women spoke to Musa with shyness and manners in aid of their father  so there is nothing in the religion that forbids this.
Women would also speak to Abu Bakr, Umar and beforehand the Messenger of Allah ﷺ and he is like a father figure (to his nation ﷺ). If there is a need and there is no fitnah this is something else.
Likewise, a judge may need to summon a woman and hear her statement. In this case, she must speak to him.
If necessary and free of fitnah there is nothing in the religion that forbids this.
 وَلَمَّا وَرَدَ مَآءَ مَدْيَنَ وَجَدَ عَلَيْهِ أُمَّةً مِّنَ ٱلنَّاسِ يَسْقُونَ وَوَجَدَ مِن دُونِهِمُ ٱمْرَأَتَيْنِ تَذُودَانِۖ قَالَ مَا خَطْبُكُمَاۖ قَالَتَا لَا نَسْقِى حَتَّىٰ يُصْدِرَ ٱلرِّعَآءُۖ وَأَبُونَا شَيْخٌ كَبِيرٌ
[And when he [Musa peace be upon him] came to the well of Madyan, he found there a crowd of people watering [their flocks], and he found aside from them two women driving back [their flocks]. He said, “What is your circumstance?” They said, “We do not water until the shepherds dispatch [their flocks], and our father is an old man.”
Answered by: Shaykh Abu Bilaal Al-Hadhramy – may Allah preserve him
Answered on: 2 Rabbi Al-Awal 1441(30th October 2019)
Translated by: Abu Sufian Saami ibn Daniel Al-Ghaani