I'm sorry OP, this all sounds very hard, especially as you're suspicious of his motivations.
I think it would be good to get recommendations for an experienced family law solicitor who understands what might be awarded in similar cases, particularly ones with a child with a developmental delay and such a clearly established primary carer. I also think its noteworthy that he has in the past suggested he doesn't entirely agree with the diagnosis - that's how I'd interpret the fact he thinks its all your 'fault', and that he has said this to professionals. I'd definitely be cautious about that, and want it written into any order than he was committed to following the expert advice/taking her to appointments/etc.
I did fairly extended breastfeeding myself (to 2y4months) and DD co-slept with DH from about 12 months to 2 - it was our compromise so I could night wean, she was definitely getting worse sleep so it meant we could separate out the 'waking because there's milk on tap' and 'waking for a little cuddle/reassurance then going back to sleep.' So I'm not anti-either, and understand your feelings. However, I think it would help you to get realistic legal advise on what is likely to happen so you can both work towards the easiest possible transition with your DD, and hopefully suggest a longer scale transition to your DH that might be agreeable to him and work for you all.
So - I would start with the paediatrician, and get advise on what kind of therapeutic nursery settings might benefit her, how to ease her in, what age/timeframe she'd suggest from a purely therapeutic point of view. I'm afraid as others have said, it may actually be that they think, say, 20 hours a week could be beneficial to her sooner than you think, though I agree 8 hour days may be considered long. If you got this information, would you trust him to contact suitable nurseries and speak to them together?
I think its worth you thinking through your pros and cons and dealbreakers as well: so if your legal advise is he's very likely to be awarded what he asks for, or awarded it within 6 months/a year.... is it worth you spending a large amount of money in court to fight it? At that point, looking at long term security for your girls, you in a better housing position and agreeing up front a slightly longer transition period even if its less than what you want might be the better option than getting an extra six months of status quo and bankrupting yourself in the process.
Breastfeeding and co-sleeping were I think part of having an incredibly confident child who is happy in full-time nursery in our case, so I understand where you're coming from. But ultimately we didn't go for natural term breastfeeding because I wanted another child, wasn't getting pregnant while breastfeeding (despite regular cycles etc etc) and felt it was a factor, and a younger sibling would be more beneficial. So I started a very slow, gentle, encouraging to wean process when she turned two that took about 4 months and resulted in an entirely tear-free end to feeding. She literally never asked again after our last feed, I still can't believe how well it went. However, I both don't think she would have stopped then if it hadn't been encouraged, and don't think it was at all negative for her. You're obviously in a very different situation, but again, if the likelihood is this is what will happen, it might be best for all of you to be in control of the journey. In all honesty I know a lot of people in extended breastfeeding circles, and I do think in some cases the idea the child will naturally self-wean at a point that is beneficial to them can be overstated. I know kids who have, but I also know a couple who needed parental intervention, and were totally fine with stopping but it was never going to be child-led. Its really difficult OP, but I think the most important thing is knowing the most legally likely outcome and not falling into the trap of assuming it will be the 'right' one, just one you'll have to work with.