What are the halakhot pertaining to a get, in a situation where the wife refuses to accept it, if the husband is not only looking to remarry, but intends to do so out of the faith, and/or a lower level of Judaism?
The husband is essentially still free to remarry, but as he is clearly not concerned with what conventional orthodoxy will say of his potential children or relationship, can/is the first wife forced into acceptance of the Get?
When a relationship between husband and wife terminates, the proper course of action is that a Get should be given by the consent of both parties. The religious level of one or another of the partners is not a factor in this, and the important thing is that the Get should be given to break the husband-wife connection.
If a wife refuses to receive a Get, she can be “coerced” into doing so by means of various measures, which are taken by the Israeli rabbinate (and to a lesser degree by Batei Din around the world).
Receiving a Get is in the interest of the wife too, of course; both partners want to move on after their relationship has terminated, and a Get is the basic requirement for doing so.