If I were you, I would ask your less preferred firm, whether you can transfer to one of their other vacation schemes (the earlier the better as with notice this is more likely than if you ask last minute). If they say no, you could even ask your preferred firm the same question. You will not be rejected/have your offer reneged for asking whether it is possible to change dates, it is a completely fair question. Personally, I think you are entitled to seek as much information as you can from both firms to make the best decision for your future.
If both firms say it is not possible, then you will have to choose your preferred firm unfortunately.
With regards to your second question, I would do what is best for you. Some people drop out because they have completed and have accepted training contract elsewhere (as well as for other reasons).