。
She has a vacation home by the sea.
Literal
She [topic-は] seaside [at-に] vacation-home [object-を] is-having.
持っている is the standard way to say 'have / own' in Japanese — bare 持つ would be the punctual act of picking something up, while ~ている expresses the steady state of possession. 別荘 specifically means a second home or villa, distinct from one's main residence. In postwar Japan owning a 別荘 — typically in a scenic spot like 軽井沢, 箱根, or by the coast — became an aspirational marker of upper-middle-class life, especially in the booming 1980s. Many were quietly sold off through the long economic stagnation that followed, but the word still carries that aspirational ring.