Personally I would leave her free in the main tank, that is cycled??. You may well loose some fry but you run the risk of losing all the fry and the mother, if you leave the situation as it is.
Stressing her is the main reason they hold off or abort. If you take some precautions in the main tank, you can greatly increase the amount of fry that survive. If you have some fake plants, bunch them closely in one corner and it will provide the fry with a hiding spot. Cover the intake with a prefilter sponge or pantyhose. Keep the other fish well fed but watch your water quality. Over feeding will need extra/higher % water changes. By trying to save ALL the fry, you could end up with little to no fry. What is the plan for all the fry anyway, have you somewhere to grow them out, the 10g??. Mollies have a heavy bio-load, not the fry initially but they will as they grow and they grow pretty quick. You are going to have to get that 10g cycled. Can you transfer some media from the established filter. You could even use some gravel from the cycled tank. Put gravel in some pantyhose, place in the uncycled filter, touching your 'new' media and this will help transfer BB. Leave the gravel in there for a few weeks and it should cycle the 'new' filter. It should be enough BB for the fry, and the BB will grow as the fry grow. Just keep testing the water.
To trigger her, you could try a large water change, 70% and upping the temp to 80. If she is ready to drop, this can help her...