Firstly you are not abandoning them because you can't be arsed. There's a world of difference between having to make a tough choice because of an illness and just walking away selfishly.
When my ex & I split up, after a few years I decided to move away with the kids. They now see her every other weekend and during holidays. Our kids certainly don't feel abandoned by their mum. She's very much a part of their lives.
But there does come a point where practicalities must override emotions. If your ex can offer them a stable loving family home whilst you will struggle to do it full time because of illness then perhaps it is the right decision to make.
It's better the kids see their mum for a few days whilst she's happy and ok than struggling every day and miserable.
In my situation, I could offer the kids a stable family home whilst with my ex they'd have been struggling on benefits and par for the course with my ex, lurching from one crisis to the next. Not an environment I wanted my kids to have to deal with on a daily basis.
So now they travel the 100 miles every other weekend and spend some quality time with their mum rather than have to put up with the lack of money, friends and latest crisis she's always going through.
Plus at your kids age, soon they'd be able to catch the train themselves. My eldest is 14 and they've been going on the train for a while now.