definitely the player.
have you got bluetooth? if so then save it to your phone and stream from there. I definitely don't get gaps on my iphone.
as for USB in the car. IMO it's always good to have a spare stick in the car so it gives the family something to listen to as not all of them are into the board member mixes I have on my phone
Modern audio equipment, even what is found in cars capible of playing digital files, do not add to latency you hear between lossy encoded tracks on albums where seperate tracks are meant to segue from one to the next (mixed, sequenced, or progression-based music like classical).
The little tick you hear between tracks that have been ripped as individual tracks and compressed down to lossy formats is an artifact that is introduced during the encoding process. There is a small bit of silence padding that is added to both ends of the single track which causes the tick or gap. Some people don't even notice it, but it drives me insane.
If you are really interested in it, go check out the wiki page on gapless playback or you can go through endless pages about it on the afterdawn forums.
This is why when you purchase a mix from beatport or even if you download it illegally from one of the "scene" groups, they are ripped in single file format.
Your only options are to rip it as a single file if you need it in a lossy format, or rip it into lossless which doesn't introduce the artifact. It literally has nothing to do with hardware at this point. It was an issue long ago when the first generation of devices came out that could play digital audio files without the use of a computer.