Cutting loose in this context means to let go and have fun. She was seen dancing in the video. She let go of work, or anything she had to do, and decided to rather have fun and dance to the song. Hope this helps!

Hi Rogue :-) The mom was really enjoying herself without worrying about what other people were thinking of her. It’s having fun and being your funnest “self” without inhibitions. If someone were to “cut loose” at a party, they could be dancing freely, socializing without anxieties, singing, etc. I hope that helped 🤗

It could mean that the mom was free, she let loose and she did not care about anyone when she was dancing.