A Spyder (or any trike with the paired wheels up front) ridden by someone who's reasonably skilled & comfortable with the handling characteristics should be able to corner a lot faster & safer than any rear wheeled trike & even many 2 wheeled motorcycles!! nojoke
As others have said, use your outside foot to push your weight over to the inside of the bike, pull on the inside bar to aid that transfer of weight & lightly balance the pull with a push from your outside hand & don't strangle the handlebars or drag them aggressively, & then smoothly guide the Spyder around as you power thru the corner.
Many people fall into the 'trap' of trying to copy what they think is the faster 'racing line' by braking hard, cutting in too soon, & then not being able to see around the corner or accelerate out of the corner as early as they should if they'd just hold out wide on the corner entry a little longer..... On a Spyder, if you do that misguided 'racing line' thing too aggressively or too fast the Nanny will sap power & maybe even add some braking to keep things under control; often leaving you with a repeated bump-lurch feel as you make a heap of little bites then straighten then bite then straighten again on your way around the bend!! You should try to practice what's often called 'Late Apex Cornering' instead.
Briefly, 'Late Apex Cornering' means you go wide early, get all your braking over while you are out there, then instead of aiming for the apex of the corner & trying to ride thru in as straight a line as you can, aim for an apex that's a bike length or 2 later so you can see further around the corner earlier & get on the gas earlier too as you smoothly let the bike ease out of the curve, effectively just 'clipping' the verge or centre line on the outside exit of the curve where the road begins to straighten out again & making a long gentle curve of it all instead of a 'straight line' with some fairly tight corners on each end. Doing this properly lessens the tightness of the whole curve so you don't hafta slow as much in the first place, let's you carry a higher speed thru the less tight curve at the same time as reducing the tightness of the turn-in/out or
any part of the curve so that the nanny is less likely to interfere; and lets you get on the gas earlier so you can exit the curve & hit the straight travelling even faster than the sure-footed steering of a reverse trike will let you if you just wander thru the corner or bump/lurch your way around in a series of little but too hard bites at it while the nanny brakes & releases repeatedly!!
But don't rely on just my poor explanation of all that, type 'late apex cornering' into google, then check out the pics & have a read - the site
www.turnfast.com has a good explanation, lotsa pics, & even some vids & graphics in their /tech_driving/driving_cornering section, well worth checking it out!! And this is NOT JUST for those people who want to drive fast or even race (altho it can help them too) it will lessen the cornering forces on EVERY corner you use it on, improve your tire life by making it easier on them, & could probably improve your fuel economy too - but most people end up using any savings there by riding a tad faster anyway!! Many of those record seeking long distance economy riders & drivers practice this style of cornering & reap the benefits in fuel economy improvements; while most of the faster race drivers & riders out there learn & use exactly the same technique to gain seconds in lap time as well by increasing their corner exit speeds - which means higher overall speeds down the straights!!
Everyone can benefit from 'late apexing'..... if they bother to try, but our Spyders & their greater inherent stability & cornering ability can make for some blindingly fast cornering; getting it down pat & making your cornering that much more relaxed & smooth just adds to the enjoyment, the safety factor, & lessens 'interference' from the Nanny!!
