Ya... deffinitly. Your elbows should be kept out and you are probably not holding tha bar wide enough.

An awesome Tricep movement is close grip bench press where you keep your elbows in and your grip real close. Probably what you have been leaning toward.

Because your triceps are smaller than your pecs as a muscle group in general - you will notice your bench weight will increase doing it properly. You will probably be able to add another 20 lbs or so to the bar depending on how off your form was.