If Carleton is charging you full price, other institutions likely view your family as not in need of financial aid/deserving of a negotiated lower price. No harm in trying, though.
More important, as a parent you should sit back and think carefully as to why this child of yours will attend college. If it’s to obtain an education, Carleton is likely the strongest option. If your goal as a parent is to succeed in paying the lowest cost of attendance, then you already know that UConn is the choice. Utimately, though, what is your student seeking?