OP try to ignore the posters who are winding you up, they are leading you around in circles and distracting from the helpful ones.
So to summarise, you have concerns regarding your DSD:
- she hardly ever actually spends time with her DM. She gets passed around from pillar to post instead.
--> Can you say a little more about this? As in, does this happen EVERY time she goes to her mum's? 90%? 50%? One in three days/nights? Every weekend night but not weekday nights? Does DSD frequently stay with the same people/have the same sitters, or are they mostly random people?
This makes a big difference. It could be that her DM simply has a more lively social life than yourselves, which is ok. If she goes out one night in three that she has DSD, and usually DSD stays with/is looked after by the same people, with the occasional stop-gap alternative, then there is no reason to assume that DSD is being negatively affected by this arrangement. If in contrast, her DM goes out 2 out of 3 nights that DSD is with her, and leaves DSD with random, ever changing strangers, I would consider DSD to be vulnerable to attachment issues, to abuse and neglect.
So how much is it effectively, and who does really look after DSD those nights?
- the house is cold and food not what you believe she should be getting.
Again, can you tell us more - who feeds DSD when her DM goes out?
--> Apart from that, not much in this.
- DSD co-sleeps with her DM and DM's new boyfriend.
This is worrying, and I'd work towards getting this to stop. Your DSD is vulnerable, from what you write, and it is often vulnerable children who find themselves preyed upon.
However, how often does this happen? Seeing as DSD rarely actually stays with DM but is passed around to random other people? Or does it happen when DSD is being babysat at DM's home? In that case, perhaps suggest to DSD that she should ask whoever is sitting for her to move her to her own bed once she has fallen asleep in her DM's bed. As a stop-gap until you can figure out a better, more permanent solution.
Ok so you have these concerns, and it is a bit difficult for us strangers on the internet to judge how bad it is as you are using dramatising language (NEVER when you probably mean 'sometimes') and you have been distracted by some posters, so you will have to decide for yourself how bad it is, or give us internet strangers some more calm info if you want help in judging how bad it is.
If you find it bad enough for things needing to change (which your OP implies), there are two strands of action you (that is, always, your DP with your support) can pursue. You can try to get DM to change, and/or you can go for having DSD with you more nights.
Neither will be easy, and I for one can't help you with this. But several PPs have given useful advice, time to listen to them rather than responding to those who are attacking you for things you aren't/haven't said, and making you all defensive about your own choices rather than pursuing what you came here for, namely advice on how you can improve the situation for DSD.