I can understand everyone's position here. I get that the parents don't want to drive 3 hours up and back in one day. They are there to see their sick mother, and who knows what kind of care and decisions may need to be made?
I understand that the boy has a mandatory practice commitment, and that coaches may be unwilling to bend for a family emergency if they get this sort of request all the time from different kids. I understand that he wants to (and should) see his ill grandmother and not say, "Sorry, Granny, I have baseball."
I understand that your daughter thinks she is ready. I think it depends on how long she has been driving and how long it's been legal for her to drive with a passenger who is not licensed and over 21 (that's what our state law is - I don't know what yours is). Has she done highway driving before? Is she comfortable with high speeds and tractor trailer trucks?
I would ask where the boyfriend is staying for 3 days while his parents are away. Is someone staying in the house with him? Can that person go along and help with the driving?
I think engine trouble is not a big risk. They have cell phones, I presume, and hopefully you have a AAA membership for roadside emergencies. I think the issue is much more the strain of driving, the distraction of a boyfriend (or any friend in the car), and night driving. To me, driving isn't about being able to steer or stay in your lane - it's about being able to focus, getting enough sleep (which teens are notoriously bad at) and being mature enough to really anticipate problems (looking ahead for construction or traffic tie-ups, passing cars, dealing with trucks and people speeding, using the rearview mirror to watch for emergency vehicles and tailgaters).
If you think it's really important for this boy to see his grandmother and stay on the baseball team, you could be the bigger person here and go along to share the driving. Yes, it's a long day for you, but you could split the driving, give her some highway experience, and really help out this family. Take a book and go sit in a local coffee shop or library while the family visits Grandma. And consider that it might not be appropriate for your daughter to be visiting the grandma - it really depends on how well they know each other, how sick Grandma is (which is probably a lot, since the boy's parents are staying for several days), and whether this is too personal or unwanted by Grandma. So perhaps your daughter should do something with you while the boyfriend visits her.