Defending sleep training to mother-in-law

Hey there fellow moms/dads/parents,

So our baby is wonderful, EXCEPT for her sleeping habits. I tried being a gentle parent for the first 7 months and letting her run her own schedule. She slept when she was tired, we got her up when she cried, and I never knew what to tell anyone who watched her in terms of a routine/schedule. I assumed she'd fall into a routine and we could reinforce it. Well, that resulted in her only ever taking 20-40 minute naps and she'd still be waking up at least twice every night up until she was 7 months. My husband travels for work so this finally broke me (a full-time working remote mom) in addition to the holiday stress I was trying to manage with no nap breaks and still getting interrupted sleep at night.

My husband and I finally started sleep training (cry it out method) after the holidays when we were both home on a break. It went great and we finally started getting 1-2 hour naps in addition to mostly uninterrupted nights.

Well... Back to reality. My mother-in-law watches my baby two days a week. The first day back, I left a note with our new rules and routines. Not only did my MIL make fun of the fact that "I left INSTRUCTIONS for her grandchild", but I'm pretty sure she totally ignored all the rules the first day back. Since I had appointments, I wasn't there the first day back.

The second day, I worked from my MIL's house like I normally do. Sure enough, my daughter woke up from her nap at the 40-minute mark. My MIL was pacing around and groaning with every single cry. She tried to argue with me that it was an hour because she took the baby upstairs sooner than when I mentally started the clock on the nap. I said no and told her to let my daughter cry it out because she usually falls back asleep within 10-15 minutes. Parents... I kid you not, I was watching the clock. My MIL groaned for 7 minutes, than got dramatic and said "I can't stay here and listen to this! I have to take a walk!" She slams the door and leaves me there with my baby. I timed my daughter and sure enough, she was back asleep after crying for less than 15 minutes. My MIL was gone for like 30 minutes and then tried to come back like "oh, I had such a headache! I feel better now!"

I had no idea what to do with that, so I kind of just ignored her the rest of the day and then decided to take my baby home early when she showed signs of being tired for her second nap.

On our way out the door, my MIL made a comment about, "I hope she sleeps well for you! I know you won't kill her, but I just don't like that."

I know I'm the mom. I know I'm in charge. My husband is on the same page as I am that we are the parents and his mom is wrong to have done that. So there's no worry about my husband defending his mom's actions. He knows she's wrong in this situation.

My question for you is: how have you defended the cry it out method, especially to in-laws? I feel like my MIL was on the verge of accusing me of child abuse. I'm happy my daughter didn't fight the nap harder that day - there's been days when she's cried closer to 45 minutes before falling back asleep. I told my husband that I'm not trying to take the baby away from his mom, but I'm having a harder and harder time justifying her as a caregiver for two days a week. Especially if she's tapping out after 7 minutes of the baby crying. Have any of you navigated a similar situation? What would you recommend/not recommend?

Thank you.