She sounds similar to me after having DS, don't think I've ever spoken openly on MN about how bad it got here. DH was doing what he could but he was caring for me and a newborn and the flat turned to shit, it was a hazard, we were just lucky DS wasn't crawling. It was disgusting, tbh, it's still not great, but it is safe at least now.
SS were wonderful, while we didn't take them up on too much, they did give us the emotional support we needed. They also put us in touch with others that could help, and when things got tough again after we'd been signed off they were on the other end of the phone when I needed help again. There was never any talk of taking DS away, not even temporarily. It was all about helping us manage.
I personally wouldn't move her back to yours OP, I know in my case I needed to learn to cope in my own home, taking me out of it would have given me a break but I'd have fallen back in to old habits the moment I returned.
Sounds like she's hiding from everything, especially with the bags of clothes. It's a normal reaction and a hard one to break. I've heard really good things about home start though, they might be able to help her break things down into more manageable chunks. Problem is when it all piles up it becomes harder to even start tackling it. Easier to just close eyes and pretend it's not there.
How easily can she talk to her gp? Might be worth her upping her medication or even changing it if it's no longer working for her?
Tbh I wouldn't count on the HV for much, if she can't talk to her then it's not going to achieve anything getting her to come out.
Counselling would probably help the most, though I know it's hard to come by. Would she accept you going to the gp with her to act as an advocate? It's possible she plays it down in front of the gp, so they may not know how serious it's got.