it would be okay for you to gift her $16K and your spouse to gift her $16K and then loan her the extra $8K. however that $8K should be evidenced by a note and have repayment terms that are enforced. fail in this last step and then you face the issue of not filing a gift tax return.
really makes no difference if you gift her the money or pay it to the dealer but it should only be $32,000. so it's probably better to give her the money. separate checks from each of you.
i would say that if you really want to give her the whole $40K. then you will have to file gift tax returns for both of you using up $4000 of your over $12 million lifetime exemption. but this seems so much simpler for all involved.
if you can claim your daughter as a dependent those other items you mentioned would likely be considered support which is not a gift.
