@Shocker @Ms. 12 Gauge has the personal experience to back up what she types!
"Naturally cost will always be a concern but I’d be curious what other folks have done with their diminutive shooter companions." Begs the question just how "small" is she? With shotgun "fit" having a LOT to do with "LOP" (Length of Pull--the distance from the butt to the trigger guard), folks with shorter arms often find a Youth Model easier to swing since they can reach the fore end w/o stretching. Add gas operation or inertia-dampening recoil systems, and a light 12 gauge with "lighter" factory loadings (1145 fps) ---like Remington Gun Club and the like--- will recoil less.
I used to shoot Trap with a 12 year old using his 12 ga. Youth Model gas operated semi. In less than a year he could easily break 20+ birds per round. You get your wife a gun that fits HER and some instruction, and she'll be kickin' yer butt in no time
Searching for lower recoiling trap & skeet loads requires a small "education":
Knowing how to read Dram Equivalent's for one. Scattergunnin' loads are still referred to in BLACK POWDER "Dram Equivalent" and the lower the number, the slower the pellets move out the barrel. 2 3/4 Dram Equivalent is common in low-brass 12 ga. target loads, and 2 1/2 Dram Equivalent is common in 20 ga. low-brass target loads. The faster loadings are "Field Loads" designed for hunting, and are often 1250 - 1400 fps and have higher Dram Equivalents. A Dram is a unit of measure that was used back in the day of black powder shells and Damascus Twist barrels. Hunting loads for pheasant (as an example) can come in both 2 3/4" and 3" magnum shells. They're all "High Brass", which means the end of the shell where the headstamp is has extended brass to absorb the higher pressure (higher Dram) loading. These will recoil MORE, and are sometimes packaged as "Handicapped" loads in 7 1/2 and 8 shot sizes. So be careful not to buy those, as they're intended to shoot Trap from the 25 yard line (9 yards further back from the Trap House than the standard 16 yard line).
NUMBER OF PELLETS:
In the "race" to gain an edge, target loads with 1 1/8th oz. of birdshot hit the scene decades ago. They have more pellets than the 1 oz. loadings, and will recoil S L I G H T L Y harder than the 1 oz. loads as the lighter loads need a little less powder to get their shot column out the tube at the same speed (1145 fps light target loading for instance). It's simple physics. Every action has an EQUAL & OPPOSITE reaction. The reaction is felt recoil, which is mitigated by weight of gun, gun action, proper fit on the shoulder, etc.
I have female friends that can outshoot me. They find it easy to break 100 straight clays. Their guns FIT them
My Daughter in-law Amy hadn't shot clays in about 2-3 years. Father's Day I took the family shooting at Old Bridge R&P. She picked-up the gun she was taught on---my Beretta Youth Model 20 ga. gas gun---and after the first two birds she broke every bird thrown for her---like a dozen in a row! Then she let her husband (my son) take his turn & miss a few! That is until he compensated for poor "gun fit".
Hope I've been some help!