Not sure about the distance however I love Marbella, well worth a walk around. There are ample buses and easy access to trains. Have you booked airport transfers. If not using the train and buses are simple and so so much cheaper than the taxis.

There are no trains to marbella, the tracks stop at Fuengirola. There are buses although after living there 15 years I never used one so can't say about the times. By car marbella is about 35 mins from carihuela so allow longer for buses. It is worth a visit but remember there are really two marbellas. The traditional old town (my favourite) and the bling bling of Puerto Banus which is about 10 minutes further along the coast. I don't think you would have time to do both unless you have a car.

Several options from La Carihuela....
You could catch the Torremolinos/Marbella bus from Torre bus station, but you have to get to the bus station from La Carihuela first, either by walking or using the bus, or you could walk up to the coastal road and catch the bus to Fuengirola, which takes about 40 mins and then the bus to Marbella goes from Fuengirola, which takes about 1¼ hours, or catch the train to Fuengirola from Montemar station and then the bus.

IMO: Puerto Banus is ok for a visit, but it's all bling with half pint millionaires up to their necks in debt behind the bling, and I don't like the attitude of some of these people and the way they speak to the Spanish waiters, as if they are something they'd scrape off the bottom of their shoes, but I'd best not go no further down that avenue.
If you like boats, it's worth the visit, but personally I would rather go up to Mijas or Benalmádena Pueblo, and before anybody says owt, yes I know Mijas has become a tourist trap, but it's still a nice place to visit without the ridiculous prices for a cup of coffee that I was charged in Puerto Banus, just because there were a few boats moored up opposite, and I see no point in going all that way to walk around El Corte Inglés, when there's one in Malaga.!

Sanji

Gosh there is a big difference in the timescale between car and bus, would be best hiring a car.

We were disappointed when we went to Marbella/Puerto Banus. We probably expected too much as we were hoping to
see Rod Stewart! I think the Marina in Benalmadena is far better and prettier. I would also recommend a trip to Gibraltar.

I would also definately recommend Gibraltar