Phew, you guys both have a lot to work on at the most fundamental level. None of the advice below is specific to shiek, because shiek isn't your real problem.
Cut dash attack completely. It's clear that it's a bad habit of yours so you need to revoke it before you can bring it back in properly. Every time you want to dash attack, SHFFL a nair and shine, that should take you quite a ways.
You both roll too much. It looks like a Smash 4 game. Just stop shielding, in melee you can dash dance, use it! Try playing games where you don't shield at all, dash away instead. Learning not to shield un-necessarily is on important step in speeding up your gameplay. Stop rolling, it follows naturally from stop shielding so much, but if you must shield, learn your full range of options. Shield grab, shine out of shield, and wavedash out of shield are superior to roll in most situations.
If shiek likes to jump in neutral (to fair, as your brother likes to do a lot), laser it. Learn your short hop lasers, you don't use them often enough to control your brother's movement. Your brother noticeably freezes when he starts to get lasered, take advantage of it, spam the **** out of him.
Go work on your tech skill dude!
Edit: Sorry if that sounded harsh, it wasn't my intention. It's just that Melee is a game of options and without putting the work in you'll be playing with your hands tied behind your back. Limited options means limited things the opponent must consider which means you are a problem easily solved.