You are with a SO who has kids.  He wants those kids in his life.  You knew this when you got involved.  We all knew that.  His kids are going to sleep over, you are not getting him all to yourself and with your child.  We all feel the way you do.  But that not steplife 

Don't control if they should sleep over or not.  Your DH should make them feel like this is there home. And you sleep in your home.  BM must be causing this or not helping at all.  If you make kids at the age 3 starting control things as where to stay, bed time, what food to eat  you are going to be for a long hard life.

i hate to say this  but when you married your DH didn't you know or think about the CS payment, gas for picking them up. Exter food . Ect.  Hate to break this to you, the older they get the more expensive it gets. Cell phones, name brand clothing, school trips, sports paying membership and equipment.  Then the prom college cars weddings   It's actually cheap now

This is not going to be the answer that you want but, the sooner their father becomes firm with them and tells them that they have no choice and are just going to have to get used to it, the sooner they will settle down and get into a routine.  He is not their friend and they do not get to make their own decisions regarding custody.  It is very likely that their mother is telling them that they can make "choices" or similar phrasing and that is what is causing the problems.  Children respond to rules and schedules at 3 and 6.  Being given too much choice makes them insecure and uncomfortable.

Especially with your own child coming, you will want to get this nailed down now.  You will not be wanting to deal with tantrums over them having to be at dad's house in late pregnancy and with a newborn.  He has a right to his custody time and if he has to go to court to enforce it then he needs to do it sooner rather than later or BM will jerk him around forever.  Then you will have bigger entitled brats on your hands.  Trust me, you do NOT want that!  Good luck to you.

You both could make or break this, they are very impressionable so hard as it is you could make it so much fun for them they'll temp forget about bm or, you could reinforce the emeshment by leaving it be. Depends how you and your partner want it to go... Treble hard being pregnant though, granted 

Yes, it is fair to force them. They are young children, they don't get to choose if they want to spend time with their Father or not. DH needs to work to make them feel like they want to spend time with him in his home. I say this fully acknowledging that BM may be working to make them feel the opposite.

You referred to "sleepovers" and said your home wasn't their home - that is part of their problem. They are your DH's children - so his home is their home. They are not having sleepovers at a friend's house, they are spending time with their father.

Did you ask why SD wants the shower on to sleep? Is she used to sleeping with some sort of a "white noise?" If so, try running a small fan - that will achieve the same effect.

What are you and DH doing to prepare them for the arrival of the baby? Are their sleeping arrangmentgs going to have to change? It would be a good idea to start putting a positive spin on the baby before the birth.

I would follow your DH's lead on this one. If he ask your opinion,  give it only once. Otherwise disengage from his parenting with his BK's. More then likely BM has been planting some poison since learning of your pregnancy (I could be wrong) to or around the kids. Either way you don't want any reason to become the scapegoat or stressed out during your pregnancy. 

It's fair to force them to stay overnight with dad. It's not fair of mom to manipulate them to the point they think they don't want to stay.

Time with dad is not a sleep over but actual parenting time. This is their home too and that's where they sleep. Get a white noise machine for the one who wants the shower on.  As others pointed out, it's not about being "fair," it's about being firm and an actual parent.  Kids don't get a choice in all matters.  

Courts order visitation for NCPs to have time with their kids. Kids are not "forced" to visit.  Kids are forced by CPs to not visit. Over nights are part of that CO.  Beyond SO enforcing his visitation there is no discussion. The only unfair thing is that BM is loading these kids up with a head full of crap that is manifesting with them being "afraid" to stay at Dad's.

A change in perspective is in order IMHO.

Yes, the Skids come and they stay as the CO stipulates.  Their desire to stay or not, is irrelevant.

If BM fails to surrender them per the CO, SO needs to smack her with a contempt motion and bare her ass in front of a Judge. Every time.