"My DP is also heavily involved with the organisation of the activity and would be needed every Saturday and wednesday/another week night even if DSC wasnt attending."
Oh, he's 'One Of Them'. Someone who is so caught up in how essential he is to an activity, who gets their jollies from how important it makes them feel. Does he think if he got hit by a bus the activity would all fall apart? Of course it wouldn't, others would take it over, and most likely few participants would notice any difference (might even prefer it). Likewise, if he were the one undergoing treatment and not you, the activity would trundle on without him.
TBH, as well are making arrangements for other family members to take his son to the activity on your treatment days, he should also be giving a heads-up to the others in the organisation that he may have to take a step back for a few months and give them time to rearrange themselves for Saturdays/Wednesdays. By not doing so, he could be leaving them in the shit if the other people involved commit to other activities alongside. But presumably that would only demonstrate how truly essential he is!
I am totally incensed by his sheer insensitivity to anyone else's needs. His responses to you are gobsmackingly self-centred, and yes, he SHOULD recognise that you will need him - not just want him around, but need someone there to physically do stuff as you will be so wiped by the chemo (I can still remember my mother's sheer exhaustion from hers). You will need someone to see to you being fed, and yes you will need someone there for safety as "things can turn ugly very quickly". That he doesn't recognise your needs reflects very, very badly on him, really highlights how inadequate he truly is 
.
I know you say you don't want to push it, but you really, really have to. Spell it out in words of one syllable that you will need him to be there, and fuck not wanting to be the bad guy! Two things in the balance, your health and his enjoyment - well, duh! Your needs trump his wants. Your stepson has a whole family that can support him in this activity; his grandparents who live near the academy, his mother, his mother's family members who she can delegate the driving to.
I suspect the reason your partner is dragging his heels on this is a combination of feeling important (ooh, it has to be me, I can add sooo much more value to this than anybody in the whole wide world) and living vicariously through his son ( "it's a hobby my DP has been involved in all his life and of course hes ecstatic because stepchild has been scouted" ). Well tough shit. It's time for him to step up to being an adult and prioritising the important things. You have enough on your plate, he needs to start acting like a partner and not an overexcited schoolboy living for his hobby. Because it is the hobby he's prioritising, not his son, not really. He sucked his son into his hobby, the hobby came first.
I'm so sorry you're going through this. Not just the chemo, but the finding out who people really are when the chips are down. 