All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
In regard to entrusting a non-Muslim in divorce, then the Shaafi’i jurists stated that this is permissible. They stated in this regard a rule: “Any person who is entitled to issue Khul’ or divorce for himself is permitted to be deputized and authorized to do so whether he is a male or a female, a Muslim or a non-Muslim.”
If the situation is as you mentioned that your husband signed on the paper, then it is him who issued the divorce and not the lawyer. Writing the word divorce is one of the metaphors of divorce and divorce does not take place unless the husband intends it. The same thing applies to the statement ‘I divorce her’ as this is not a clear expression of divorce and divorce does not take place except with intention; for more benefit, please refer to Fatwa 92476.
Therefore, if your husband intended divorce with that, then divorce took place otherwise no. For more benefit on writing the word divorce, please refer to Fatwa 90056.
If we presume that divorce had taken place, then your husband having sexual intercourse with you after two days of divorce means that this happened during your waiting period. If a husband has intercourse with his wife while she is in her waiting period (from a revocable divorce), it is considered as him taking her back even if he did not intend to take her back according to the view of some scholars as clarified in Fatwa 89845. Hence, if it is confirmed that he took you back, then you are considered his wife and it is only by divorce that your marital relationship with him can come to an end.
Similarly, what we mentioned about the writing of the word divorce applies also to the e-mail that he sent to you informing you that he wants to end the relationship with you. Divorce does not take place unless he intended to issue divorce when he wrote that and this seems very unlikely. For more benefit, please refer to Fatwa 82541.
Allaah Knows best.