Assuming the parent has a fixed width, e.g #page { width: 1000px; }
and is centered #page { margin: auto; }
, you want the child to fit the width of browser viewport you could simply do:
#page {
margin: auto;
width: 1000px;
}
.fullwidth {
margin-left: calc(500px - 50vw); /* 500px is half of the parent's 1000px */
width: 100vw;
}