PostgreSQL JDBC transaction isolation - postgresql

Question

I have these two operations:
public class Car {
...
public void delete() throws SQLException {
Connection c = Db.getConnection();
c.setAutoCommit(false);
if (c.getTransactionIsolation() == 0) {
c.setTransactionIsolation(c.TRANSACTION_READ_COMMITTED);
}
String sql = "DELETE FROM cars WHERE id = ?";
try(PreparedStatement s = c.prepareStatement(sql)) {
s.setInt(1, id);
s.executeUpdate();
c.commit();
}
}
}
and second one:
public class CarTransfer {
public static boolean transfer(int person_id, int car_id, int other_shop_id) throws SQLException, Exception {
Car car = FindCar.getInstance().findById(car_id);
Person person = FindPerson.getInstance().findById(person_id);
try {
if (car == null) {
throw new CallException("Car doesn't exist");
}
} catch (CallException e) {
System.out.println(e.getMessage());
}
Connection c = Db.getConnection();
c.setAutoCommit(false);
if (c.getTransactionIsolation() == 0) {
c.setTransactionIsolation(c.TRANSACTION_READ_COMMITTED);
}
String sql = "";
try {
sql = "UPDATE car_belongs_shop SET shop_id = "+other_shop_id+" WHERE car_id = "+car.getId();
} catch (NullPointerException e) {
System.out.println("Did not find a car / shop");
return false;
}
try(PreparedStatement s = c.prepareStatement(sql)) {
s.executeUpdate();
try {
if (person.getCredit() < 100) {
c.rollback();
throw new CallException("Not enough credit");
}
else {
if (car == null) {
c.rollback();
throw new CallException("Car doesn't exist");
}
else {
c.commit();
person.buy(100);
}
}
} catch (CallException | NullPointerException e) {
System.out.println(e.toString());
return false;
}
}
c.setAutoCommit(true);
return true;
}
}
So what I want to do is to transfer a car from one shop to another. But in that time, some other transaction can be done on the other side, when someone removes that car from database (that's first method delete()). What I want to do is to block any delete() method in the time when transfer is running. I'm trying to do that by this code, and it's transaction isolation (in level read committed). However, this does not work as intended, because it's still possible to remove a car whilst transfer method is running. Can you help me, whether I use sufficient isolation level or have whole transactions in the right place of the code?