How to deal with other tourists taking pictures of my children?

This is not the answer you were looking for, but the fact that lots of people have been taking pictures of your children suggests that your family stands out too much in comparison to other tourists.

You may get angry and yell at some clueless foreigner who doesn't even speak English or Spanish and scare them away, you may hire a lawyer and make a living hell for a random childless lady/guy from the the other side of the globe who just thought your kids were cute and who has no money to defend themselves in a legal battle against you, but neither of those options will prevent your privacy from being invaded again and again by other people.

This leaves you with only three obvious options:

• Avoid tourist spots when traveling with children. Because reasonably speaking, I highly doubt your daughters are the ones who have any "say" over where your family goes and would much rather enjoy something more fun rather than visiting some ancient monument under a scorching sun, or a top-ranking beach filled with people to the brim.
• Don't make your kids stand out that much. Using modest clothes and a stroller may help, to a certain extent.
• Accept that you have no privacy. While it may feel unpleasant and invasive, there seems to be very little real threat in what other people do. Very few real criminals would act so conspicuously if they were to present any actual threat to your children.

Coming from Portugal, where there are very similar laws to Spain, unless you are a well known person in a public place (actors, politicians), you have your right to privacy supported by law against being filmed or photographed in public places.

Furthermore there are additional regulations protecting the privacy of minors and creating additional complications even for their family members posting images of them in social media.

While other tourists might have not, locals also have some pretty good awareness of those laws and might even assist you. People are usually friendly and overly protective of minors well-being and safety as a rule. People are also relatively conscious of their right (and others) to privacy.

So I would say on those cases were photos your children are actually the goal of an insistent and rude photographer, if in Spain [or Portugal], be very vocal for attracting the attention and possibly enlist the help of local people. You might actually threaten to call the authorities in addition.

Coming back to Spain Ley Organica 1/1982, 5th Of May contemplates your right to privacy, and Ley Organica 1/1996 from 15th of January, lawful protection of minors reinforces the right to privacy of minors.

"Article 4 Right to honor, privacy and self-image

1. Minors have the right to honor, personal and family privacy and their own image. This right also includes the inviolability of the family home and correspondence, as well as the secrecy of communications."

Carry a camera and take photos of the photographers. Since in most countries it's not illegal to take photos of anything in a public place, you are at liberty to reciprocate. Some may not mind, and the others have no proper reason to ask you to stop.

It would appear that some have missed my point. Those who are doing it innocently will not mind their own photo taken, whereas those with other issues probably would, and if that's the case, photographic 'evidence' has been taken. It would probably stop those who knew what they were doing wasn't above board.

As far as doing this in a country where it's not legal anyway - come on, think more deeply!

Since this question is not tagged for Spain, and it is tagged for cultural-awareness and local-customs, then be aware that in some countries (including England and Wales) photography in a public place is generally unrestricted, and your principal recourse in such situations is not to go into those places, or to leave if you're getting annoyed at the photographic activities of others.

From http://www.photographers-resource.co.uk/photography/Legal/Access_Rights.htm:

Generally you have the right to photograph anywhere that is public property, including public roads, footpaths, rights of way and between high and low tide at least if not the entire beach areas throughout the UK ... No one, other than a police officer who takes it for evidence, can take your camera away, and they are supposed to just take the card rather than the camera if you have taken it out of the camera , and no one can insist you delete photographs taken

I've been that stranger. I once surreptitiously took a photo of (native) people in a rural Swedish village who I throught were dressed funnily. A young man noticed, and responded with a gesture of moving his finger across his neck. The villagers belonged to a religious sect that prohibits photography. Another time, I took a photo of a stairs in Stockholm. There was a person on the stairs who I did not take note of. The person very much did take note of me, and reprimanded me, telling me not to take photos of people without their permission. After these two incidents, I have improved. When I can avoid it, there are no people in the foreground of my photos.

The people taking photos of you or your dependents without your or their permission should stop doing so. Regardless of the legal situation, it is not right to take portrait-like photos without permission. There is little you can do beyond what the Swedish woman on the stairs did: firmly tell them not to take photos of people without their permission. If they're like me, they might learn, and you'll have helped the next person.