The code makes more sense with your explanation, though some parts are confusing. That aside, if you have not tried it already I would recommend that you remove the FORCE INDEX part, and see how it perform without that.
Then if you have not tried composite keys, you can give these a try:
ALTER TABLE car_bussy
ADD INDEX datecomposite (date, registration),
ADD INDEX datecomposite2 (registration, date);
Then take your query and run it directly against the database with EXPLAIN prefixed, either through MySQL WorkBench (if you dont have this free database manage software, I strongly recommend to download it), or through phpmyadmin etc. (NOTE: when you know which of the two that is the best match for your table, remove the other one, as each index take up space and will slow down insertion/updates to the table)
EXPLAIN SELECT b.date, b.registration AS registration, o.city AS city, o.address AS address, o.id AS id
FROM car_bussy AS b
LEFT JOIN car_entry AS e
LEFT JOIN objects AS o
b.registration = '[the info]'
AND b.date = BETWEEN '[from date]' AND '[to date]'
AND e.id!='[the id]'
If you are uncertain what this does, and how to read the output take a look on this article: