I know that at this stage in the relationship you will only see the good in your girlfriend, and that's a great way to feel - I'm sure we all look back on those first years of being in love very fondly. Before the inevitable 'but', though, I want to say that I'm not in any way saying that she is not as lovely as you think she is - obviously I don't know her and couldn't possibly judge her.
However, regardless of the amount of money involved, if you give up your house, you are putting yourself under her control so much more than if you had the security of a house of your own to return to if things don't work out. You would also risk alienating your daughter at a time when she needs you and, presumably, has taken you at your word about letting her stay in the house until she has finished her studies.
Also, you are each coming to the relationship with 'baggage', which is inevitable after the age of about 30. If things are going to work, you both have to make allowances for one another's children, financial circumstances, housing situation and so on. That doesn't seem to be what is happening, though. If your girlfriend is resentful of your daughter and granddaughter after two years, how will she feel as the little one grows up?
What are the arrangements for her own children? Are they going to be staying in the joint house? If that is the case, what is she planning to do to compensate your family in order to keep things as 'fair' as she says she wants?
You must be having doubts, or you wouldn't have posted. Trust your instincts - this is not right (particularly where your daughter is concerned), and I wonder if you know this in your heart of hearts. Tread carefully?