there will be multiple nests. at least one outside, and likely one inside. professional help is quite useful indeed.
you don't need to destroy the tree to control the ants inside, a good investigation should reveal the holes inside the tree where the ants keep coming back to. chip around until you hit the soft, mushy spot, and spray a can or so of ant killer in there. you will get a short-lived spray of ants out of there, and if they're carrying the yellowish bulging queen, so much the better.
an arborist will generally then dig out all the crummy wood and backfill with mortar or cement.
there are probably several nests in the tree, so that side will bear watching.
a professional is probably the best way to go for the inside infestation, and recommendations on sealing up the ant entry.
sig: if this is a new economy, how come they still want my old-fashioned money?