I added my kids as authorized users on one of my oldest cards (Discover) at a young age and never gave it to them. It was They did get a card as an AU of our Capital One card when they traveled aboard so to avoid the foreign exchange fee.
When it was time to apply for a credit card their own, it was instant approval. Their first card approval on a card of their own was Discover. They didn't have jobs yet. They used the monthly allowance they got from their parents, which was never verified by anyone.
I think you can add your MIL as an AU on your oldest card to establish her credit as well, assuming you have excellent credit, and never even give it to her.
My parents added me to their AMEX card when I was 18 yo, but it aged my credit history back to when I was 3 yo. To this day, my credit history shows starting when I was 3 yo. When I apply and and approved for new AMEX cards, it shows I am a member since the year I was 3 yo.
My parents still have that original AMEX and I am still an AU even though I never use the card. They still pay the AF which is very low because it is grandfathered. I don't know if it will change my member year if they ever cancel the card but I have established excellent credit of my own, so I'm not sure 50 years vs 35 years of credit will make a dramatic difference, if they ever cancel the AMEX Traditional Gold.
Anyway, once you add her as an AU and it shows up on her credit report, she can apply on her own. You have to check to see which credit card companies report it. I know that AMEX and Discover did for us but things might have changed in recent years, as this was more than 15 years ago for us.
I might start with a Discover card as well. No annual fee and simple cash back with revolving extra bonuses.
Good luck!