Can her husband forbid her to speak to her daughter from a previous husband who is not Muslim?

If this daughter of yours was Muslim from birth and you are both Muslims, and she is the one who has apostatised from her religion, then the apostate has no sanctity in Islam. Rather he should be asked to repent from his apostasy. If he repents, all well and good. But if he does not repent, then the ruling according to sharee‘ah is that he is to be executed, if there is an Islamic state that can do that. 

But if the situation is as we see, that there is no Islamic state that carries out the hadd punishment for apostasy on the apostate, then at least we should shun him, express our dislike of him and disavow him until he comes back to his religion. If he comes back, all well and good, otherwise he has no sanctity and has no right for ties with him to be upheld or good treatment. 

This is reinforced if your husband tells you to do it; you do not have the right to go against him in this regard. 

Ibn Muflih (may Allah have mercy on him) said: 

Ahmad said: … If there is someone who becomes a disbeliever or commits evil by practising innovation or calls people to misleading innovation or an evil innovation, the one who is unable to argue with him and prove his mistake, or is afraid that he may be influenced by him or be harmed by him has to shun him. And there is another view, which is that he should be shunned by all, and this is the apparent meaning of the words of Imam Ahmad quoted above. Ibn ‘Aqeel stated that this (the latter view) is the correct view in his book al-Mu‘taqad. He said: So that (shunning him) will bring him back to his senses and make him recant and come back to Islam. 

He also said: If you want to find out the extent of people’s commitment to Islam nowadays, do not look at the crowds around the doors of the Jaami‘ mosques or the noise they make in ‘Arafah when they start to shout “Labbayk”; rather look at how easy-going they are with the enemies of Islam. For example, Ibn al-Raawandi and al-Ma‘arri, may Allah curse them, lived for many years writing prose and poetry (that contained heresy) and now their graves are built up (as a sign of respect) and their books are widely circulated and this is an indication of the weakness of religious commitment of people. 

A similar fatwa was issued by Shaykh Taqiy al-Deen ibn Taymiyah (may Allah have mercy on him).

End quote from al-Adaab al-Shara‘iyyah, 1/255 

But if you and her father were originally not Muslim and you used to follow the religion that she follows, then Allah guided you to His religion but she continued to follow her religion, i.e., she was originally a disbeliever and is not an apostate, then there is nothing wrong with you upholding ties with her and talking to her, and you should come to an understanding with your husband concerning that. Perhaps Allah will guide her at your hands and open her heart to Islam. 

Al-Bukhaari narrated in his Saheeh (5981) that Ibn ‘Umar (may Allah be pleased with him) said: ‘Umar saw a suit of striped silk being offered for sale and he said: O Messenger of Allah, why don’t you buy this and wear it on the day of Jumu‘ah and when delegations come to you? He said: “This is only worn by one who has no share (of reward, in the Hereafter).” Some suits of it (that fabric) were brought to the Prophet (blessings and peace of Allah be upon him) and he sent a suit to ‘Umar, who said: How can I wear it when you said about it what you said? 

He said: “I did not give it to you for you to wear it; rather sell it or give it to someone else. 

So ‘Umar sent it to a brother of his in Makkah before he became Muslim. 

Imam al-Bukhaari (may Allah have mercy on him) included this report in a chapter in his Saheeh entitled Baab Silat al-Akh al-Mushrik (Chapter on upholding ties with a polytheist brother). 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) narrated that one of the scholars said: 

Shunning is of two types: shunning in the heart and shunning verbally. Shunning the kaafir is done in the heart, not loving him or cooperating with him or supporting him, especially if he is in a state of war against the Muslims. It is not prescribed to shun him verbally because that will not deter him from his kufr, unlike the sinful Muslim who would usually be deterred by that. It is prescribed to talk to both the kaafir and the sinful Muslim by calling them to obey Allah, and they are to be enjoined to do good and forbidden to do evil. Rather what is prescribed is not to speak to them in a friendly manner and the like.

End quote from Fath al-Baari, 9/497. 

And Allah knows best.