It actually sounds like the opposite. With no seat struts, caster in the front, and a narrow rear, it sounds like your kart is setup to flex and lift the inside rear quite a bit.
Are the other karts you’re referencing all Tony Kart 401s? Because different manufacturers will have vastly different setups to achieve the same end goal.
The tendency for new drivers is to grossly overdrive the kart, resulting in similar complaints about lack of grip. Have you tried to adjust your driving at all to counter the handling woes you’re feeling, in other words, slowing down your entry speed and attempting to get back on the throttle earlier, driving through the corner.