I definitely think it will be warm enough for sea swimming. Many of the hotel/apartment pools are heated otherwise they might colder than the sea if not in direct sun. You might be mindful of the strength of the sun in Oct with young children.
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Spring and Fall are cooler and dressing in layers will help you cope with the temperature changes. But note that whilst it may seem warm and pleasant on a sunny day, the locals won't be in shorts. If you want to blend in then dress as they do – with long pants, sweater, scarf and a jacket with sturdy shoes or boots.
The island's desert-like climate means whatever time you decide to visit, it's almost always warm enough to swim and get a tan. In October and November, daytime temperatures vary between 22°C and 27°C, and the Atlantic Ocean stays at 19-22°C year-round.
Clothes. In the early part of fall, from September to about halfway through October, you can still wear summer clothes. You can get away with tank tops, shorts, and spaghetti straps. At this time of the year, temperatures fluctuate between hot and mild.
While temperatures can heat up over the summer, October weather offers a slight chill in the air and can sometimes be warm enough to take a dip in the Mediterranean Sea.
If you plan to visit Spain anytime between late October and late December, then you should definitely pack jackets, sweaters, thick socks, scarves, and other warm clothing. Stick to dark colors like navy, black, and brown if you don't want to stand out as a tourist.
The cheapest time to visit Spain is usually from December to March, though you can also enjoy affordable flights and hotels in early spring and late autumn. The winter months see many vibrant markets and activities dedicated to annual celebrations such as Christmas, Carnival, and New Year's Eve.