It is a very generous offer and the savings are massive.
How long have you lived indpedently? I am sure your parents will be fine with your coming and going but you are going to have to be more careful with when you come home and checking in so you don't wake them up or worry them.
Saving money on rent is balanced not only with smaller living quarters and family, Mom, Dad, and brother, but a longer commute. You already don't like the commute you have now. Is an increase going to be worth the money saved? It is not only additional time away from your boyfriend and the things you like to do but now it is additional time you cannot spend working on the new house or time you need to rest and relax.
And there are cats to think about. Can you introduce your cat to your parents and see if they get along? You adopted the little one and made it a part of your family. If he is going to be unhappy for a minimum of two years is it worth the stress to him?
And you are going to end up doing more around the house and probably paying some of the utilities. You know that you are likely to feel like a freeloader if you don't.
If it were me, I would say thanks but no thanks. My Hubby would go nuts, he likes having his own space. I would have said thanks but no thanks before I was married as well. I love my parents and have a great relationship with them but I value my independence. Toss in the additional commute and I would really say no thanks. I changed companies to avoid adding 20 minutes onto my commute. I value being close to work so that I have more time with my family and for sleep.