I enjoyed Ubeda (my base), Baeza and Jaen (I thought the least interesting of the three), but staying somewhere other than Jaen in that part of Andalucia does present transportation challenges. I bussed to Ubeda from Madrid, side-tripped to Baeza and Jaen by bus and went on to Cordoba by bus. The buses were perfectly comfortable but not very fast. That area would probably be a bit cooler than points south, and those cities have a different look to them, in addition to having far fewer tourists, which is always pleasant.
In addition to the places you list, I spent 3 nights (of 29 in total for Andalucia) in Cadiz, taking a day-trip to Vejer de la Frontera by bus. I skipped Jerez, but it's easily visited from Cadiz (or vice versa). Just looking at the map, I think Jerez or Cadiz would probably be better jumping-off points for Arcos de la Frontera than either Ronda (as you are considering) or Seville (which I chose for a reason I no longer remember--it might have been related to bus frequency, since Ronda's a bit closer to Arcos than is Seville). Although I love nice, long stays in my base cities, I don't like having to take two or more side-trips to the same area; I'd rather peel off a few nights to spend in that target area. I acknowledge, however, that the trains will get you from Seville to Jerez or Cadiz reasonably fast.
From Seville I took a day-trip to Carmona by bus. As noted above, I also took my Arcos day-trip from Seville (bus) rather than from Ronda.
Bus service from Ronda isn't frequent, so you must be very careful about the schedules. Days of the week matter, and you can't afford to overlook a local holiday that will (probably) be treated like a Sunday for scheduling purposes. I have not been to Olvera. I considered seeing Zahara de la Sierra but discovered the bus schedule simply did not allow a day-trip from Ronda to Zahara; one must spend the night. I did manage a day-trip by bus from Ronda to Grazalema.
As you have figured out, the legs into and out of Ronda, with stops/side-trips to some white villages, are where you might benefit from a short-term car rental. I've never rented a car in Europe so I can't comment on how much time that would save you, but I think for a family of four this is approaching no-brainer status unless you don't have a driver who's OK with narrow, curvy roads, etc.
I have so far managed to avoid the Costa del Sol except for Malaga (quite a nice, though large, city), but I took two side-trips from Granada, both by bus: Priego de Cordoba and the Alpujarras. You may have fairly unrelenting heat during a June visit to Andalucia, in which case a day in the Alpujarras might be a welcome respite. It's off the heavy-duty tourist path, and there are some opportunities for town-to-town walks. I mention this because you have enough time, I think, to indulge in some quieter, more subtle pleasures.
I note that you have more days planned in Granada than in Seville. Seville is a lot larger and has more sights, so I'd be tempted to shift a few nights unless you anticipate making multiple day-trips from Granada down to the coast. However, if you're unlucky with the weather, Granada (at altitude) will probably be somewhat more pleasant than Seville, temperature-wise, even aside from the proximity to the Alpujarras and the Sierra Nevada.