What sort of furniture is she offering to give you? What purpose will they serve in your place? Do you actually need the items? Do you have the space for them?

If the furniture she's offering to give you isn't actually useful, and if it can't replace the drawers or desks in their usefulness, then why not just decline taking their furniture? Perhaps part of the furniture your mom is giving you, she views as having more use to you than what you do have, and maybe she just doesn't think it would all fit into your home?

Because if you need the chest of drawers and they aren't planning on giving you anything else to hold your clothes in... it makes practical sense to keep the drawers. Although I don't know why you need two different desks - do two different people use them? Did your sister GIVE you the drawers, or did she give them to you on a conditional/loan basis?