R is being totally unreasonable.
It smacks of him wanting 'his' time on paper - nothing an be varied, as he 'loses' time, when in fact, this isn't time he was spending with dd3 anyway since she is at an activity,
The starting point for all this, is the longstanding commitment dd3 has made to her sport. 4+ years, not inconsiderable for a 7 year old. I am guessing that this is the longest running commitment out of all the children (if I have their ages vaguely right!)
In all large families, there is compromise. Child 1 gets the first pick of activities, due to age and circumstance, but then as soon as another child comes along, compromise is needed somewhere. Sometimes this is the other parent stepping up, sometimes this is a non-preferred arrangement for child 1 (e.g. dropped early, or a lift share), sometimes extra running around for parents (to drop early/at lift share's house) etc.
There are 6 children in this equation, so it's never going to be simple, and that's without 3 different parent groupings.
BUT
dd3 wants to keep going with her sport. This is important for health and personal development. And crucially, it isn't a new arrangement which is eating into her contact time, it has always been there (so R cannot compa,in on this score)
Despite a very busy morning, with lots of different children/activities/places, all children currently get a good 'quality time' morning, whether an activity, 1:1 time with a parent figure, or soft play. There is no 'hanging around' for any of them.
R has been offered at least 2 reasonable offers to accommodate his drop-off issues. It is understandable that he doesn't want to lose the Friday afternoon/evening contact, but this could be worked around easily by him dropping dd3 off on Saturday morning, rather than demanding OP does the running around (to suit him!), which actually then makes it 3 reasonable offers.
The only person being obstinate here is R. He doesn't want to continue with the current arrangement, because ds1 want some to try an activity. Ok, fair enough, compromise needs to happen. But R doesn't want to lose contact time, doesn't want to drop dd3 off with her mum on Saturday morning, doesn't want to enable a lift share. R doesn't want anything other than dd3 to give up her activity for half the time, give up competitions, and to be bored hanging around watching her stepbrother(rather than have the option of a quality morning as all other children get).
It just doesn't stack up.
Why is R acting so negatively towards dd3? Even worse when you consider that dd3 is R's own child.
Why does everything have to be about what everyone except dd3 wants?