This and any type of bad behavior will effect your DD.   BM isn't going to help, as in she is not going to change,   It's DH responsibility to parent his kids.  He must let them know there is two sets of rules. One is BM... totally out of your control and  Second side of route that applies to your home.  first time your rules are broken. Some type of punishment,  start early show you mean it.     
unfortunately DH Parenting time may become a punishment time not a fun time.  That the unfortunate effects, instead of normal family life. As in intact family's. There some game/activity period then back to getting ready for the next day.  SF use the visits as all fun thing to do.  I grew up in a intact family and our weekends were not packed with fun activities. My friends were going on adventures every weekend   

You need to start parallel parenting.  That means dad's house/mom's house.  What happens there stays there.  At 4 and 5 you can start them , they will get the hang of it.  This would be my hill to die in with DH.   I'd also recommend giving the skids an hour of time to readjust to being back at your house.  I let my bios just chill in their room.  Recognize to them that they are transitioning between homes and the rules at your house are different and you will give them time to remember them.  Praise them when they remember to behave, encourage the good , but let dad deal with the bad.  
 

BM won't like like it, when she starts complaining and try's to insert herself into your home, DH just needs to hold his boundary and ask her if she wants him to insert himself in her home.   
 

Bottom line is they will influence your bio, it's up to her parents to make sure it's good stuff, and up to dad to make sure all of his kids know the standards and expectations for behaviors and hold each one accountable.  BM might wage a loyalty war and the skids might stop coming over as teens, if not sooner.  Don't let her crazy take over your home.  
 

I don't miss those days.  

I agree with the above. Kids adapt to different rules in different locations all the time. Each new year, they get a new teacher. Rules in the library vs rules at the playground. They will be fine with 2 sets. Since they are very young, they are trainable. Make it fun, not punitive. Instead of saying "You didn't flush the toilet, you are bad!", when they don't flush (or do whatever they should be doing), tell them "We flush toilets here because it's clean and good manners. Next time, i want to see that you flushed." When they do, tell them "You flushed! You have such good manners!" 

I remember being a kid and being from a different part of the country and then moving to the Deep South. Rules and customs were different, and at first i was confused why teachers or babysitters would get mad at me. If BM is letting them act like animals, it's up to their dad to teach them how to act and what to do. They may have to be taught right alongside your kid. Now, if your DH doesn't see the need for them to behave differently, that would be the real problem. ETA with the ages being that close, the skids' behavior will affect your kid's. These skids need to be taught better. 

My advice from personal experience having my own 3yo daughter and 12 month son vs SD10, SS12.. is when they carry on (and they do act stupid at this age!) I immediately segregate DD3. I distract her with something she enjoys like me colouring in with her or me playing a game with her and leave the skids alone for DH to deal with. 
I then educate and reassure DD3. She is usually confused why all of a sudden she can't play with her older siblings, and I explain to her their behaviour is not ok, and I tell her the reasons why including how disrespectful it is. If I let her continue to play then I'll have to issue warnings, and time out. She immediately understands and then is happy to play with her colouring books. 
Eventually the ferals come downstairs as they are bored again and try to engage with her I explain their boundaries (no jumping on couches and wrestling) and DD3 understands and won't even attempt it, they usually pout and storm off looking for DH. 
Goodluck it's exhausting but it works for me and I don't give any effs what they think anymore. I tolerate no bad behaviour. 

You cannot fix what goes on at BM's home.

What you can do, and what we did, is clearly define the standards of behavior and performance that Skids will be held to in your home from the second they arrive until they depart to head back to idiot BM's.   Your kids need to see the rules applying to their elder half sibs just as those rules apply to your little ones, in an age appropriate manner.

Elder spawn cannot be allowed to pollute the lives of y ounger sibs with toxic bullshit.  

So, do not tolerate it.  You and your partner cannot fix BM's family situation and life but you can protect your life and family and should.  Do not tolerate his failed family progeny dragging BM's lack of parenting crap into your home and family. Immediate compliance. Period. Dot.

IMHO of course.