Does the Hampton inn crosstown center have access to the T line? If not what is the transportation option to Boston children hospital from hotel?

The hotel shuttle will take you there.

You can always use Uber or Lyft. It would probably only be around $8 each way.

Yes it does. I think it has a free shuttle to and from the hospital area.

I dont know for sure but the hospital complex is rather large. You could try contacting the hotel directly.