i would highly advise against putting tape on the wires or cutting them. i couldn't think of anything worse to do to a snare drum, really. if the snares aren't vibrating evenly then there's a problem with either the snares themselves or the snare beds on the drum (ie: they're not laying flat).
some of this is "that's how it is". snares are going to rattle when loud noises around them happen. that's just what they do--snares vibrate and they rattle. you'll pretty much always see this when you kick the kick. if you tighten the snares some, you can cut down on this, but be sure not to choke the drum. also, it's possible that the kick is resonating at a frequency that's an octave or two down from the pitch of the snare. try retuning the kick or snare just a tad to see if that fixes that.
if the snare and tom are pitched too closely together, hitting the tom will make the snare resonate almost as loudly as if you'd hit the snare instead of the tom. this is called "sympathetic resonance", and it's b/c the two drums are too close in pitch. the solution here is to tune one of the drums to a different pitch.
as the pitch of the snare is typically the more "important" of the two, i'd get the snare where i want it and then tune the tom so that it's out of the way.
moongel and such are good for final adjustments in terms of ring, etc (although i'd never use duct tape), but you really need to get the drums in tune first....
cheers,
wade