If she stays in her playpen quietly why not just let her do that ? I don't understand an hour nap for someone that young but I wouldn't change your schedule , I would just let her stay in the playpen till nap is over .
I have a strict 1-3 quiet time , I know how hard it is not to be able to have down time and did terminate for a non sleeper but it was only one day a week care .
Could you try her down earlier to allow for cry time ? I am a huge fan of CIO and used it on my dd at 16 months , let me tell you it was way more than 20 minutes she screamed .
But now even at 5 , she is a dream to put to bed !!
My suggestion would be feed her abit earlier and put her down , the furthest from everyone and shut the door and walk away , no checking until its quiet ( unless she can not see you )
Crying is healthy too , as long as she is safe I would let her go and not get her up until the proper time .
I usually start on the first day , doing exactly how I want her schedule and by the time a weeks over they usually are on board !!
Hope it works and you get some gown time do you don't burn out ! Also I wouldn't be telling her mom , this is your home , your business , your not being mean or cruel children need rest !!'