Absolutely ridiculously stupid to attempt to divorce without legal advice when there's children and/or property involved - it will cost you far more in the long run not just financially.
Your uncle really should have made this clear to you and should be able to recommend a good lawyer and if he can't ask around for local recommendations.
Your ex is completely taking the piss.
While not guaranteed I too would not be surprised if you were to learn there's an OW involved. Be prepared for her to be pregnant too - that might be the motivation for his rushing you & his desperate need to get a decent property.
Other than that no way is he interested in actually parenting 50% he's just trying to dodge paying cm.
With that in mind AND the fact they only backdate to date you first claimed you NEED to put in a claim now. If you decide later to trust him with a private arrangement (I wouldn't) you can, but if you delay making a claim now you could end up screwed over.
Re his family backing him up - if thats just based on him telling you don't take it as truth. My ex tried that crap, I learned it was the complete opposite! His father gave him an almighty bollocking and his mother slapped him! Then gave him an almighty bollocking! In my case there was an OW, he tried to make out she was welcomed with open arms, truth was she wasn't welcome in their home until the baby produced as a result was born and only then grudgingly. Her (ow's) father upon learning of the situation found him at his local and also gave him a slap. Ow's mum gave him an absolute earful too, again he wasn't welcome in their home until after first baby born and again grudgingly. When OW parents found out (because I told her and showed her proof) that he was delaying the divorce (in order to delay marrying her) HUGE blowup again. Ow's sister and ow still barely speaking to each other over 15 years later because sister disapproves of how they got together, and how they've behaved since, they were previously close. so don't believe all you're told.
Glad to now read that you're getting good legal advice.
But please try and be prepared emotionally for there to be a possible ow, I hope not but there must be a reason for his trying to rush you etc