All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
Divorce does not take effect by sending an sms (text message) without holding the intention of issuing a divorce. This is because writing the words of divorce is a metaphor of divorce with which divorce does not take effect except if it is accompanied by the husband's intention, as we have previously underlined in fatwa 89894.
The ruling on signing the divorce papers is as you have learned from the fatwa of Shaykh Muhammad ibn Ibraaheem Aal Ash-Shaykh; the divorce does not take effect by signing them, even if someone else wrote the words of divorce.
Your wife has no right to force you to divorce your other wife or threaten to request a Khul‘ and seize the children from you. Verily, this is wicked and blameworthy. Abu Hurayrah, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, forbade the Muslim woman from bringing about the divorce of her Muslim sister in order to “spill what is in her vessel” (i.e. deprive her of the blessings that she has). [Al-Bukhaari]
An-Nawawi wrote, “The meaning of this hadeeth is that it is not permitted for a woman to ask a man to divorce his wife and marry her instead so that she becomes his only wife on whom he spends and who enjoys his kindness and with whom he has intercourse, etc. Depriving his first wife of these blessings was metaphorically described as spilling what is in her vessel...” [Sharh Saheeh Muslim]
If your second wife is a righteous woman, then keep her and try to appease your first wife and pacify her.
Allah knows best.