This isn't a black and white issue to me I'm afraid though I must caveat this by saying that I do not have experience of chemotherapy at all bar an odd film and a friend who went through it recently but rarely spoke about it as she had an adult daughter and SIL who lived with her to support her.
I was a single parent until my dd was 4. My first and foremost loyalty therefore has always been to her. I was all she had which made us very close. I had family who were entirely reluctant to offer any support whatsoever. When she was 4, I met a man (he had no children himself). He found it very difficult to come to terms with the fact that I was fiercely loyal to dd and would always put her first. In the end he turned out to be an abusive prick but that's a story for another day and not entirely relevant here. What I would say is that your relationship, though you're living together, is relatively new. It's 3 households involved in a way, not just one.
This is not your DP choosing a hobby over supporting you. It's him prioritising his son and being inconsiderate at worst. You yourself have chosen to pick a day for the chemo to prioritise your own biological dd which will have the least possible disruption to her life and that is fine and understandable. I would do the same.
You are two combined families who have come together as one, which makes things difficult.
You might need to make adjustments to find the least worst option for both children. You don't want your dd to see you while you're unwell, he does not want his ds to lose out on this invaluable and rare opportunity.
The solution to this will lie in calling in favours from all angles perhaps and it will likely involve compromise on both sides. It might mean that you change to a Thursday or a Wednesday. Speak to the experts to find out when you're most likely to need actual support and experience the worst side effects.
Cancer or illness of any kind doesn't just throw you a curveball, it throws a fucking nuclear bomb into your entire world. It is horrible, evil and cruel.
I am not an evil person but my DP a few years into our relationship appeared very depressed. After a couple of days or weeks (can't remember now) he confessed that he was hearing voices telling him to kill himself. I called 111, got him an out of hours appointment and sent him off to the appointment on his own. Bear in mind I had a 6 year old asleep in bed upstairs with school in the morning. I then went onto a website similar to MN while I was waiting to hear back. Jesus Christ but I was crucified! Apparently I should have been with him. How could I be so cruel and uncaring? What I wasn't accused of isn't worth mentioning. He was given a referral letter to go to the psychiatric hospital immediately (this was about midnight at this stage) so passed by and dropped in on the way there (hospitals were in different directions from our house). There had been some supportive posts and when I updated the thread, another pile on. I had no fucking choice though, short of ordering an ambulance or something and at that point I had never had any dealings with anything medical involving transportation or similar. He drove to the hospital and was admitted until he was well. He was very hurt that I couldn't visit but I had a commitment to my dd and he had the car (30 miles away)
So what I'm saying is that I can see both sides of this. I've also been very unwell and same ex-DP was utterly brilliant to me. But this is not a simple matter. When children are involved, my instinct would be to prioritise them before anything and that means both of them, not just your own dd.
I hope that I haven't offended and I'm sorry that you're having to deal with this. Don't necessarily write him off. He might care deeply, but feel like he has little options available to him.