I'd say no too.

IMO, transition period are more for the Mom's peace of mind then the child's needs esp at 12 months old.

If she doesn't want to be "that Mom" then she needs to stop behaving like her.

Stick to your guns. When you next make contact be firm. Offer her the dates which suit you. Outline what your transitions comprise of. You are not a cafe for her to pop in when she wants it to happen esp since you've already stated that it's too soon. The last thing you need is a stressed-about-going-back-to-work new mom eagle eyeing your every move as that's disruptive to all.

Dear xxxx

Although I do understand that leaving your child with a new carer is a very unfamiliar and stressful time for the parents, my usual transitions take place 1-2 weeks prior to the start date.

This has proven to be the most effective timing. Too soon in advance means the child won't remember the transition and so it's effectiveness is completely lost.

Although I appreciate your offer to stay with your child, this is not helpful as it's very disruptive to all the other children when a stranger is present in the day care.

With this in mind, I have scheduled XXX date for an introduction which is the week before your start date. If you would like to drop off your child at xxx time, and then say a brief but firm goodbye and return to collect him/her at xxx time. Based on how your child is in your absence, should I determine another brief period of time in the day care would be beneficial, I have tentatively scheduled this for xxx day at xxx o'clock. "

Be firm. This is your business and if you don't run it, it will run you. People like this can run right over you so you need to show her from the beginning that you are the one in control.