Can I request a DNA test for paternity during divorce?

Yes. If paternity is in question, then it is imperative that the issue be raised in the divorce. The court will always grant the request as long as there is a reasonable basis for it, and it will probably divide the cost equally between the parties. If paternity is an issue and it is not made part of the divorce case, once the divorce is granted, the child is deemed to be that of the husband, and it will be very hard, if not impossible, to undo later.