I’ve just caught up with your more recent posts OP. Mothers aren’t supposed to be best friends, they are supposed to be mothers. You want to think yourself lucky she hasn’t tried to step into being his mother, just his best friend.
I can understand you feeling you are ‘losing him’ but it’s not a contest. There aren’t winners and losers among the parents.
Step-mother and his Dad presumably spend a lot more ‘quality time’ with him as he’s there most of the weekends so they will likely have more contact with his friends’ families too.
It’s interesting you were happy for Dad to have him every weekend when it suited you to go out at the weekends but now he has a stable and happy relationship with his Dad, Step-mother, and sister, who are his family, you feel left out.
For information, a huge percentage of Every Other Weekend Dads work during the week but their children’s mothers realise weekend time is precious and expect to share weekends. You didn’t because it suited you to go out at weekends. His Dad took his chance to see his son every weekend while you partied. Did you drop the rope or just not realise that your fun weekends and holidays would come back to bite you on the bum ?
Their financial position is irrelevant; you can’t buy time and love.
Sorry, you may not be able to, in your parlance, ‘win’ him back. At least he still sees you but don’t blame him for declining to go on holiday with you when you’ve only just realised you want to take him on holiday. Why the change now ? You don’t even seem to want to give him a holiday he would enjoy, only one you would enjoy, why ?
I’m not sure it would be a good idea to pursue having him some weekends now because he is in such an established routine he may resent being away from what he regards as his family.
You may think I’m being harsh but, from the information you have given, it’s how it looks from this angle. If you were a father who had placed fun weekends and holidays with friends above their child for years but then complained another man had stepped into being their child's best friend or even parent they would be slaughtered on Mumsnet.