If you are referring to finish routing the 1.5" edge of a 20" x 1.5" long piece by using the technique of passing the part between a fence and the bit: No, do not do this. In general, you need a certain width compared to the length in order for that technique to be effective, or else you get what you experienced - the part wobbles. This is highly dangerous to try, so just don't. instead, double-stick-tape another piece of acrylic and use a flush trim bit to get your 1.5" edge where you want it.
I will say this loud and clear so there is no mistaking this
ABSOLUTELY DO NOT USE GLOVES AROUND ROTARY POWER TOOLS/EQUIPMENT
Wearing gloves will make any potential injury severely worse. Think Chinese Finger Cuffs. Now imagine your hand in one of those and a blade spinning at 25,000 RPM coming in contact.
My Dad made this mistake when running a bench jointer and finishing an edge. The glove tip got caught in the blade and pulled his hand into the blade. Luckily, it jammed the rotor and stopped it before taking off his finger. He has a scar to remind him of this incident.
No gloves. Not around table saws, circular saws, routers, jointers, band saws, jigsaws, drill presses, hand drills, really any high-speed rotating tools of any kind, and I mean any kind. That is a serious mistake that you will eventually pay for.
The answer is to pay attention and respect the tools.