Achtung, you say the new members "didn't feel welcome" ... Maybe the sisters didn't make the NMs feel particularly welcome? You have to do that. We assigned a buddy to each of our NMs - she would invite her NM out for coffee, lunch, etc. The buddies changed every week until big and little sisters were matched up. It made the NMs feel welcome and gave them a chance to meet several different sisters that they might not have already met through rush.
As far as where the money goes, how about circulating the chapter budget to the members? It can just be a top-level thing - you don't want to give an itemized budget for initiation to NMs after all

- but if members (NMs and sisters, both) know how their money is being spent, maybe they'll be more willing to pay their dues rather than balk at them.
You have the right attitude, wanting to fix things. Lots of luck!