In King Lear, why does Lear go to Albany's palace?
As the play gets underway, many events happen quickly. King Lear voluntarily gives up his power, planning to divide his kingdom among his three daughters--Cordelia, Goneril, and Regan. When Cordelia displeases her father by refusing to flatter him, King Lear banishes her and divides his kingdom between Goneril and Regan. His plan is to live with his daughters, alternating the times spent with them. Albany is Goneril's husband. King Lear goes to Albany's palace to take up residence with Goneril first, as he had planned.
The end of the first scene in Act I, however, shows that Goneril and Regan are not happy with the prospect of their father living with them. His banishment of Cordelia has made them distrust his judgment and his rash behavior. Goneril says this to Regan:
Pray you, let's hit together. If our father carry authority with such dispositions as he bears, this last surrender of his will but offend us.
She speaks what they both are thinking: they do not like their father's planned living arrangements. The two daughters agree to think about this. Goneril says, "We must do something, and i' the heat," meaning soon.
As a result, after King Lear and his attendants have settled themselves in Albany's palace, Goneril soon makes her father leave, sending him to Regan, who won't have him either.