I think the sovereign immunity claim is just to try to get it dismissed at the beginning on a procedural issue. I don't think it's likely that the jurisdiction question goes anywhere for Maryland since the ACC filed first and North Carolina definitely has jurisdiction over Maryland given their membership in the ACC over a 50 year period.
If I recall correctly the major claim on the merits is that the exit fee was actually a penalty couched as a liquidated damages clause. Under North Carolina statute (since the ACC is incorporated in North Carolina) and in most states there is a distinction between the two. Liquidated damages are a remedy built into a contract for when someone breaches the terms of the contract or wishes to terminate the deal. In this case Maryland leaving the conference was going to leave a speculative amount of damages which are difficult to ascertain. The damages in the clause are supposed to be an amount reached in good-faith to be a reasonable estimation of what the breach is costing the party to the contract who did not back out.
In contrast a penalty is a sum meant to be a deterrent for someone to breach the contract. So basically Maryland is claiming that the 50 million dollar fee was a penalty rather than an actual good faith estimate for a liquidated damages clause. If it was in fact a penalty then Maryland would not have to pay the large fee. They may have an argument, especially given the fact that Swofford has opened his big mouth saying something to the effect of "we wanted the buyout to be so much that nobody left."
Of course this is all from a 2L so I may have some, a lot, or all of the facts wrong. An actual attorney can probably answer the question better. Edited to add a few facts on the preliminary questions.