Logo revamped for clothing and social media

Hi, I already have a logo for my dance school and I'm looking to have this revamped and made a little smaller for social media designs and clothing. My dance school is called Vital Signz Dance and we have a clothing range which is shortened to VSD. I am looking for a design for VSD that can be incorporated into a pocket blazer badge for our clothing range. I hope this makes sense. I have attached the following:-

My Dance Schools Full Logo
Our shorted logo VSD for clothing
The crest that that would like our VSD logo to fit and design into