Please get a lawyer.
You must, must, must discuss this with both your daughter and her husband, in detail and frankly and openly. Please do not appeal to emotions by saying "This is your childhood home, you will love having it" or "This is our inheritance we want to give your son." A house can be a huge blessing or a huge problem. And grandson is a minor. His parents are likely thinking much more about paying his eventual college bills than about raising him in the family home for emotion's sake.
She rents right now; do they even want to own property? Some people truly do not want the costs and maintenance and taxes that come with a home; she needs to be honest with you about how she feels about that. She may love the idea of a house but want it to be her and her husband's own house, not the house in which she grew up (husband gets a 50 percent say here too, she's not the only one affected if she gets a house).
Your daughter may not want your home for many, many reasons. You need to be open to the idea that maybe she doesn't want to live in it; she would have to put money into it to fix it up and sell it; she would want to sell it but would feel too guilty to sell it and would be stuck with a house she doesn't want; she would be reluctant to keep it but rent it out -- many people do not want to be landlords, etc. etc.. But you will not know if you don't talk to her and her husband. Yes, both must be on board.
You may find that they would be much happier with your making arrangement to leave money in a real trust for your grandson when you die. A trust is a legal instrument to protect that money and if it is done correctly, the money cannot be used by mom or dad (they would be the "trustees" but could not spend the money except under VERY limited circumstances such as for specific educational reasons). Ask about a "qualified minor's trust" and how to fund one through the sale of your house when you die, since you will be short on other assets due to medical bills.
It is wonderful to think of your grandson's future, but get an experienced wills and trusts attorney to work with you. They don't cost as much as you might think. Your local senior center might be able to hook you up with one who does low-cost work for seniors, too.
If this is about the emotional side of it -- you say "This has been our grandson's second home since he was born" are you thinking along the lines of "We want him to grow up here after we are gone"? Please reconsider. That might be wonderful and precisely what your daughter and her husband want, yes! That would be great. But it might also be that your home is not in a school district that would work for their child later on; or they would have to pour money they don't have into making it liveable as they want it; or it's not a great location for their jobs, or a good neighborhood for your grandson as he grows older (other families with kids his age? amenities like parks etc.?).
I am not trying to dismiss the idea, just noting that when it comes to property and money, it is vital to talk to the folks involved BEFORE any names are put on anything. If you have already talked with her and she's on board and so is husband, fine, but ask them to help you get an attorney!
We used a wills and trusts attorney to set up a qualified minor's trust for our child with money from the sale of a house that was left jointly to her and her cousin by a great-uncle. We were VERY fortunate that my brother- and sister-in-law wanted to buy out our "half" of the house so we got cash and they got the house -- we did not want any ownership of this house which is thousands of miles away in another country, though we loved the house itself. But if they had not wanted to buy our daughter's share of the inherited house, it could all have been a mess. Be careful not to leave your daughter with a house she doesn't want, or is reluctant to sell because she feels it would be wronging your memory. Be businesslike and get professional help -- after you talk to her in detail.