I like it, through in my suggestion the 15000 soldiers included their families. But there are a few reason for the high amount of soldiers, in Europe you were usual able to call burgher militias up in case of war, here with such a large Jewish population you the state aren't willing to do that except among the Dutch, free Baster and Christian Mulatto. So a bigger than usual force are needed.
I would personal put it 5-7000 soldiers 3-4000 wives and the rest children. Beside a significant part of the soldier population hjasn't brought wives from Europe with them and have married local womens, they are usual included in the Mulatto, Baster, Ladino and population, even through their children will be included either in the Baster or Dutch population (after colour).
In economical terms I would say that the soldier are urban workers, while not being training, guard or campaign, they usual work in skilled (a significant number of the asoldier are former journeymen)or unskilled works, this are a important extra income. Their wife too works in these kinds of work. This make the soldier and their families a important part of the garrison towns economy. In many way breaking the local guilds monopol and in some of the more isolated towns the main workers in these kind of trades. As such they are important for the development of the different garrison town into local trade hubs, where the local farmers can trade raw material and crude manufactoried goods for more developed ones
I am still not sure that this is realistic, although 7000 certainly is more so than 15000. The main issues are cost and willingness/ability of the local taxpayers to afford that level of year on year commitment. I would think that outside of a quite nasty war, the colonists would not want to make that commitment.
To give you more points of comparison, the US Army numbered about 16,000 immediately before the Civil War (so far as I can tell from a brief online search) and the size quickly reverted to the mid 20,000s after the war finished.
Now, admittedly the US and indeed NZ/Australia were never very willing to pay for large peacetime standing armies during the colonial period, which seems to be something they inherited from the British, but I still don't see why the Capelanders would be willing and able to do so, outside of a long war.