First of all, there is nothing stopping you from returning to the Church given your current situation provided you and your husband live in continence until your marriage situation can be rectified (see the
Catechism of the Catholic Church, paragraph 1650).
Now, with regard to whether your current husband can seek the declaration of nullity for his previous union, he can do so without the cooperation of his previous wife.
When you approach the Church seeking a declaration of nullity, you are asking the Church a question: Was my marriage valid? The Church is obliged to give you an answer. As such, the tribunal seeks to gather as much information as possible to make an informed decision. To that end, having the cooperation of both parties is extremely helpful, but not necessary.
I would encourage you to contact your local priest to begin the process. He will direct you in all that is necessary.
Now, if your current husband is not willing to seek a declaration of nullity with his previous wife, then to my knowledge there is no way for you and your husband to convalidate (get your marriage recognized by the Church as valid) the marriage. Getting a declaration of nullity for his previous union is a necessary condition for you to become validly married.
If this is the case, I would encourage you to talk to your current husband and explain to him how important it is for you and your relationship with the Lord that you be in a valid marriage with him. And also that in order to have a valid marriage with him, he would need to receive a declaration of nullity for his previous union.
Here is a website with quick answers to questions concerning annulments:
canonlawprofessionals.com/annulmentquestions.html#Q10