RE: Help with shotgun for wife
As another left-eye dominant Southpaw, I can only agree with e4c4ever. As for the powder issue mentioned by Bronko, that is an extreme oddity, and should be checked by a competent Gunsmith (not the guy at Gander Mtn. who cleans guns & mounts scopes, but the honest to goodness trained Armorer/repairman). The breach of a firearm is designed to contain any & all safe chamber pressure. If debris or powder is escaping past the breach block, there is a problem and asafety issue.
Pay attention to what Moose said. Although his taste is a bit pricey for your budget, his selections arebeyond reproach. Hit the used racks to save on cost. Autoloaders tend to be gentler, as 1) they're heavier, 2) cycling the action absorbs some of the recoil impulse. Pump actions tend to be less money, therefore more common. Don't worry about second shots, light loads not cycling the action, etc., as you will be using this piece as a single shot for quite a while. By the time either of you is ready for Doubles or Skeet,the recoil sensitivity will be gone and/or this "entry level" set up will have been modified and/or changed significantly.
Managed Recoil& Trap loads tend to have far less energy, and energy produces recoil. Clay pidgeons don't have heavy feathers or adrenalinprotecting them, and ANY noticeable chip, break, etc. counts as a "dead bird."
Lighter weight of the 20 ga. Youth models leaves less to counter-act the effects of felt recoil, and the lesser recoil generated by the smaller guagecomes froma smaller payload of shot. Targets are less likely to be hit, as you are sending fewer pellets and a shorter shot string down range.
Back to that used pump orauto... If it's one of the "Big Name" models, you can pick-up an aftermarket stock for cheap. Add a little more weight in the butt, the best recoil pad you have handy, find your Sweetie a decent recoil shield (ie: PAST, etc.), make sure the length of pull suits her, and you're good to go. And, you're well under the $500.00 you mentioned.