Is it possible to get the coordinates of the rectangle on mouseClick, so I have all the corners of the rectangle?
See event object (http://leafletjs.com/reference.html#event-objects):
var map = L.map('map').setView([53.902257, 27.561640], 13);
L.tileLayer('http://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png').addTo(map);
var bounds = [[53.912257, 27.581640], [53.902257, 27.561640]];
var rect = L.rectangle(bounds, {color: 'blue', weight: 1}).on('click', function (e) {
// There event is event object
// there e.type === 'click'
// there e.lanlng === L.LatLng on map
// there e.target.getLatLngs() - your rectangle coordinates
// but e.target !== rect
console.info(e);
}).addTo(map);
Use e.target.getLatLngs()
.