Gosh, there are so many different things going on in your post.
From your post it seems as if the children have been sharing their time equally for 2 whole years already? What pattern does it follow now?
You say "I can't help but feel concerned for children having to divide their time and home between two houses." but ALL children with separated parents have to do this whether the divide in time is equal or whether it's one overnight a month. That's an unfortunate, but a rather fundamental and unavoidable fact of separation. It's also baffling because you are putting forward an offer where they have 6 nights with their dad and 8 with you, which is only 1 night different in quantity to what he wants.
I have seen a lot of people unhappy about their children having two "homes" and this is something I can never get my head around. Home is where the heart is and I would be heartbroken for my son if he felt like he didn't have a home wherever his father lived. Children love their parents equally - can you imagine how horrible it would be as a young child to feel like a guest in your own mummy or daddy's house, like you were an occasional visitor? No, I want my child to feel like he is always at home no matter what day of the week it is. So I agree with your ex that you should call both houses their homes.
How you imagine you would feel, as the adult you are now, is pretty irrelevant. What is relevant is how your children actually do feel about it and how they feel about wanting to spend time with two parents they love equally and that's glaringly absent from your post. What pattern would they like? I do shared care with my ex and our son has been able to articulate that from a young age. He raised the issue himself of changing the pattern when he wanted to and I expect we'll adjust it quite a few more times as he gets older and his needs change.
They key phrase in "I am always the one who takes the children to the Doctors, dentist, hospital, hair appointments, buys the school clothes, fills in forms and generally deals with most of the practical aspects of being a mum as I have always done." is as I have always done.
Ever heard the phase 'If you keep doing what you've always done, you'll keep getting what you've always got.'? It's just human nature that if someone is taking up the slack and efficiently just taking care of everything, the other person will carry on thinking they don't need to. I know it's difficult to move from being the one doing everything and being in control, but you need to let go of doing everything and pass some of this responsibility to him. I did all this stuff before my ex and I separated, but I gradually just pushed back on lots of it. It did require me to prompt him to begin with, but in 3 years he's got more and more proactive. There are a very few small 'mum' things I'm more likely to end up doing, but that's OK with me - we bring different things to the table. You also need to put your foot down, if he wants shared care, about taking time off if one of the children are ill. My ex and I share that as and when it comes up and not always according to who actually has him that day.
But on the other hand, if a father's time is restricted to mostly weekends and they go for longish periods between seeing their children, then the opportunities for day-to-day parenting (like hospital appointments) are limited and because they've missed them a lot, they'll just want to spend their time with them. It's a lot easier to demand those things are equally shared when there's no difference between the type of parenting you actually get to do.
With regards to the 5 day stretches, I think it could be on the long side for a 3 year old to go without seeing either parent, especially if it's a sudden change. We do 3 day alternating except over weekends which are always split, but I expect it will lengthen when he's older. Have you spoken to your children about what they want? Would you be willing to look at your proposed schedule again to find something that works out differently?
I think that before you need to go to mediation, you need to really work out what all your different underlying feelings because I get the feeling from your post that there are quite a few different ones in there. Forget about your arguments for a while and just work on working out your feelings - justifiable or not, feelings just are. It will help you to clarify things in your mind, might change your mind about some things and it will help you articulate your concerns to your ex in reasonable 'I statements'.