First timer Family Court

[Bellaroo17]

Hi All...i'm new to the forum and wondering if anyone can offer me some advice. I split officially from my partner 18 months ago, he was with someone else and neglected to tell me. As a result he has shown little interest in his daughter (6) since leaving, but every now and then rears his head.
Recently he has become more settled in his new relationship and is now pursuing me for more access through the courts. We have had various informal arrangements so far which he continually breaks, and now what I am proposing formally he has declined. I am attending a MIAM meeting tomorrow but he has previously been to 2 and the mediators wrongly told him I refused (they actually told me to speak to my solicitor before confirming with them, but then went ahead and signed the court forms anyway, now making me look really bad).
I haven't opened his proposals which he has done online as yet as frankly i'm too scared to but also want it formalised via a court order so that he can't continually try to break them. He is emotionally abusive, manipulating and controlling, but I'm not sure he's "that bad" that the courts will see through it all.
I'm absolutely petrified about the impending future now as I love my daughter to bits and have a phenomenal bond built up with her, which my ex denied me a lot of when she was younger. I'm scared to lose her 50/50 entirely and since he has recently moved from 40 miles away to only 4 miles, I'm worrying this is very much going to be the case.
Can anyone offer me some advice to prepare, what should I be doing, what the courts do or don't like? Are there any loopholes or good bits of information anyone can offer me? My solicitor is, I'm told, the best money can buy, but I even get the impression she things I've been too stingy on contact in the past. I want him to show some interest and commitment before giving too much, but I'm not against progressive plans at all and I've tried to show this.
If any of you could help a desperate mum I would really appreciate it. I'm not really sure where else to turn for guidance now! Thank you

Thank you that’s really helpful. Since I wrote this I have now had a MIAM meeting with a different mediation provider so am now waiting to see if he will mediate.
Completely take on board that I need to change my language and phrases to be more child based, I’m just trying to learn the do’s and dont’s of what to say! I have recently offered him much increased contact and he has point blank refused by a very strongly written email quite obviously written by his girlfriend, not him, and it’s full of lies, so I guess this only goes in my favour.

I’ve got a really detailed diary since he left us of every occasion so I’m now about to start typing that up and extracting the relevant pieces, I’m just very reluctant to relive it all!
I do agree I do think a court order is needed to ensure structure so I’m not against it, it’s just a very scary process and I ultimately don’t want to set him up to fail and let her down, but communicating that through to him is proving tough!