Vedo che la tua domanda è corretta.
Ma se vuoi selezionare in base all'ID dell'auto, dovresti aggiungere anche l'ID dell'auto come condizione nella tua query
Ad esempio
SELECT b.id, b.startDate, b.endDate, b.car.id
FROM BorrowedDate b
WHERE :userDateStart NOT BETWEEN b.startDate AND b.endDate
AND :userDateEnd NOT BETWEEN b.startDate AND b.endDate
AND b.car.id = :carId
OPPURE puoi farlo anche tu
SELECT b.id, b.startDate, b.endDate, c.id
FROM BorrowedDate b INNER JOIN b.car c
WHERE :userDateStart NOT BETWEEN b.startDate AND b.endDate
AND :userDateEnd NOT BETWEEN b.startDate AND b.endDate
AND c.id = :carId
quindi devi passare :carId value è uguale a 2
AGGIORNAMENTO
puoi provare questa query SQL se hai bisogno di ottenere risultati dinamici, lo aggiornerò presto con JPQL
SELECT b.id, b.startDate, b.endDate, b.car.id
FROM BorrowedDate b
WHERE '2017-04-02 00:00:00' NOT BETWEEN b.startDate AND b.endDate
AND '2017-04-10 00:00:00' NOT BETWEEN b.startDate AND b.endDate
AND b.car.id NOT IN (SELECT DISTINCT bd.car.id FROM BorrowedDate bd WHERE '2017-04-02 00:00:00' BETWEEN bd.startDate AND bd.endDate OR '2017-04-10 00:00:00' BETWEEN bd.startDate AND bd.endDate)
QUI ci sono JPQL anche
SELECT model.id, model.startDate, model.endDate, model.car.id
FROM BorrowedDate model
WHERE :userDateStart NOT BETWEEN model.startDate AND model.endDate
AND :userDateEnd NOT BETWEEN model.startDate AND model.endDate
AND model.car.id NOT IN (SELECT DISTINCT b.car.id FROM BorrowedDate b WHERE :userDateStart BETWEEN b.startDate AND b.endDate OR :userDateEnd BETWEEN b.startDate AND b.endDate)