So glad that your family ran the NPC for Dartmouth. That’s a great step accomplished!
As your family’s financial situation can be problematic with NPCs, you can also reach out to Dartmouth’s financial aid office and ask for a pre-read on your numbers due to those factors that make NPCs less than accurate. Most colleges will do this, and that way you know exactly what the number for Dartmouth would be.
The fact that the calculator estimated $45k and your family said they could pay $50k sounds good. My concern, however, is that your family only thinks it could do this for 2-3 years. If your family thinks that it can pay $45k for 2 years then you have a $90k budget for 4 years ($22,500/year). If you family can pay $45k for 3 years then you have a budget of $135k for 4 years ($33,750/year).
The number one reason for students dropping out of college is finances. Colleges are the biggest source of significant scholarship money. As @tsbna44 mentioned, outside scholarships tend to be relatively low dollar amounts and those that are for larger amounts are extremely competitive. Unless your relatives have said how much they are willing to give for your education, then I would not add that to your calculations, either. How would you feel if you need to transfer to a college that you could commute to from home after your sophomore or junior year at Dartmouth, if the tuition was even affordable for your family?
Ask your family how much they think they are willing and able to contribute per year for FOUR years. Give them time to come up with this number so they can check their accounts, their investment plan and financial horizon, their feelings, etc. Then develop your list of schools off of that number because, from what you mentioned above, that number doesn’t sound like $50k.