Halachikly speaking, are there additional financial obligations to the wife besides the kesuva amount? For example, paying for her apartment rental or moving expenses back to her city. Or if kesuva amount is small, should one be obligated to pay out more? Can she refuse a ghet in this instance?
My apologies that it took some time to get back to you.
Regarding your question, halachikally the husband only has to pay the kesuba, which is his obligation to her and child support which is his obligation to his children. Child support would include whatever is the accepted norm for a parent to provide for their children.
Shulchan Aruch E:H 71-1.