She does not want to go through another bad marriage

The information you have stated about this second person is not encouraging. The fact that he calls a non-mahram woman on a daily basis is cause for suspicion. It is not necessary to call her every in order to find out her opinion and her response. The promises that he spoke about may be genuine or may not be. Hence our advice to you is as follows:

Try to ask others about him, and about the new situation he claims to be in. Maybe you will find that he has some righteous female relatives who will be able to give you some useful pointers. Of course, asking questions and checking information will take time, but that does not matter, because of the seriousness of the issue. If, after you have found out about the mosque where he prays, the classes he attends, or the books and tapes he reads and listens to, you feel that he is most likely sincere and if you feel that you are able to cope with the possibility of a second failed marriage – Allaah forbid – and that it would not be too great a loss if you were to leave him after discovering that he is a hypocrite and a cheat, then we see no reason why you should not marry him. You can set out conditions and make clear requests in the marriage contract, such as requiring that he do all the prayers on time, and give up major sins like drinking alcohol, committing immoral actions, and so on. Tell him that you are going to take him at face value and deal with him on that basis. Also, do not forget to pray Istikhaarah. We ask Allaah to help you make the right decision and to guide you. May Allaah bless our Prophet Muhammad and his family and companions, and grant them peace.