Hi and welcome, Burt.
Atkins done properly, IMO, is sort of the gold standard in terms of being strict and getting the best results. If there are some mistakes you're making, switching plans probably won't help.
Neither of you has that much weight to lose. It's not going to fall off as if you're 300 lbs each. It's going to be slow. Also, if you diet was already half-decent, you won't see any drastic results.
If either of you are on any medications - even something as simple as an NSAID - they can make it extremely difficult to lose weight on any plan.
If you've been consuming any Atkins bars or anything else containing sugar alcohols, "there's yer problem." Maltitol in the bars is partially absorbed and can not be subtracted. I won't even eat them in maintenance; they give me gut cramps.
If you're looking for short cuts, try eliminating all sources of gluten and other grains. LC wraps and such aren't allowed on induction anyway, but ditch any soy sauce you've got if it's not labeled gluten-free. Avoid processed meats that contain corn. Try eliminating dairy, but be careful what you replace it with. Nut milks are out. Be sure to stick to the induction rules.
Can you give us an idea of exactly what you've been eating? Post a few days worth of menus, maybe?
Best of luck.