I am the owner of a 12 year old DD! It is hard work sometimes, but I have to parent her and guide her.
She would wear the skimpiest of shorts, the most cropped crop tops, the most full face of make up, including tiger stripes contouring, if I let her.
I do not let her. Yes, she has crop tops, but they are worn OVER vest tops! Yes she has shorts, but when they become as arse revealing as she would like them to be, they get thrown out!
She has make up, she is allowed to experiment with it, but if we go out, I attack her with the baby wipes to take it down to an acceptable level.
Your DP won't step up, so, as you are being judged as the 'mother' when you go out together, you need to sort this out, firmly but nicely. Maybe buy the girls some new, more age appropriate clothing, then let them wear their new clothes. Maybe offer to do their make up for them, face masks (the peel off type) first. Have some fun with it and them but do stick to your guns!!
I say this as someone who became a step mum to someone when she was 9 years old. I also have a DD who is 22, so have been through all this twice before going through it with DD2.
When I was step mum, my step daughter also had a mum with very blurred boundaries, but she soon learnt they were different at our house. Funnily enough, she gradually chose to spend more time with us until it was 4 nights with us, 3 with her mum, then when she was 15, she moved in with us totally. Children and teenagers actually feel safer with boundaries and rules!!