Nothing special really, just a fresh save with her overdue with a single baby.
I just applied your mod pack over the game files from the OP.
Couple of saves here. Couple of other bug thats happened is at some point is her sprite no longer walks and when I tried the rich house stuff (?), it transported me to a small room with the guy from the convenience store in there and becomes soft locked.
The walking bug you're describing is an interesting one, it's something I encountered way ages ago - it will stick to your save and survives new game plus. Not sure what causes it but equally not the highest priority at the moment.
As for softlocks, I believe it's not an uncommon thing with the rich house unfortunately. I believe people here have found ways around certain softlocks, it might be worth looking for what people have found (Papanurgling has an image describing onesuch workaround, I might include it in future patches)
As for the main bug, I've looked into it and due to the way that the expansion mod is limited in how big each overdue (single,twins,trips,etc) can be, most of the functions in terms of large overdue babies have been omitted. I have considered finding a way to put them back but it may not fit with the way the expansion mod works, so it might be easier to just cull parts of the offending mod. Either way, I'll give your save a spin and get back to you on it.
Edit: Latest version of the my patches should fix the birthing cg bugs, give it an install to fix the issue. It's not a perfect fix but I think it should behave roughly how the original did? I am considering the birthing CGs entirely if I get round to it in the future.