Know that this is a huge undertaking for you, not impossible, however. But before you take miuccia's advice, which IMO is spot on with the raison d'etre for the trip being the pilgrimage to Teramo, you must set planning guidelines with the others.
Starting with...and an idea of a group meeting (EMail back and forth is better, I think, to limit fisticuffs!) is good...a logistics come-to-Jesus discussion. Teramo is probably gorgeous, but decidedly out of the way. You only have 10-14 days. Assuming you're an Italian family like mine, you're going to have a certain number of your group that like everything set for them, go-along folks, and then a few whose attitude is 'I've never been to Italy, I wanna go where I wanna go!', with no regard or knowledge as to how to get around or whether it makes sense or not. And you have a big crowd...
If you're the lead dog here, you have to set a plan forth and when (not if) they question it, have your logistical reasons at hand. Personally, I think a week on the Adriatic, visiting Teramo and exploring nearby areas...then a week in Rome--especially if you're flying in and out of Fiumicino--in a big apartment (or series of close-by smaller apartments) is the way to go. When you're in the Eternal City--my favorite place on the planet--one can easily take a daytrip to Florence, 90 minutes each way by fast train, Naples/Pompeii is a longer daytrip but doable. But day tours within Rome itself--for those who want to participate, give everyone that option--are great. Roma is also the best wandering/sitting & people-watching city I've ever seen.
I've been to Italy three times, just with my wife, and through my love of planning we've had great times, basically a self-styled tour--not flawless but pretty good. This next April, we're taking two of my cousins and possibly another couple with us, and the planning dynamics change for sure. FYI we were able to just book a 3 BR, 2 bath apartment in Rome for $650/night. Know this--it's difficult to say 'I've checked and re-checked the logistics on this, and this is the best way' without being labelled a control freak! HA!