How do we politely turn down my future mother-in-law's offer?

My fiancee, our son, and I are planning on moving into our first place. I got pregnant my last year of high school and we have been taking care of our son and working ever since. We plan on moving so I can go to cosmetology school and he can go to college after I finish school. We know things will be tough and we will do as much as we can on our own but luckily we have lots of great support just in case. My fiancees mother has been one of the most supportive and I'm truly grateful. However she offered to give us her couch. She said she wants to buy a new one anyway. The only problem is they have a male Chihuahua that marks his territory on everything including the couch. The couch is also covered in dog hair and has "bald patches". It's definitely not the best couch to have around my son. We have saved money and plan on buying our own cheap couch/futon. My fiancee agrees with me that we do not want her couch but we aren't sure how to tell her. We don't want to upset her so we thought about taking the couch and then throwing it away but when she visits it will be awkward. How do we politely tell her we appreciate her offer but don't want the couch?