The OP describe this country as a place that practices slavery, extend slavery to mixed couple slave/non-slave, and has groups of "slave catchers" operating openly to stop 4 years-old to check whether they are escaped slaves. Somehow, I confess, I didn't picture a vibrant democracy in the first place, at least until the OP gives us more details to fill in the blanks. Plus, having border control (or, if border are more porous, city gate checks) doesn't necessarily mean being a totalitarian regime in my opinion, but we're veering into politics.
The slave snatchers didn't snatch the 4 year old to check if he was a escaped slave, rather the 4 year old's mother, who was, she's dead, is a escaped slave, this means that the country the crown princes mother comes from class's the crown prince as a slave
This means that The slave snatchers didn't snatch the 4 year old to check if he was a escaped slave, rather they had reasonable grounds to arrest him on suspicion of being the son of a escaped slave, which if their right makes him a slave
What happened is that the 4 year old's mother comes from a family were all male members have a distinctive birthmark that proves he's a male from that family, naturally he has the distinctive birthmark
1 of the slave snatchers got a good enough look at the 4 year old's distinctive birthmark for him or her, I haven't decided on the gender yet but the odds are it'll be a male, to be able to have reasonable grounds to arrest the kid on suspicion of being the son of a escaped slave
But what about his guards?, see below, and once they had him they used a spell that's unique to that country to confirm that he's the son of a escaped slave, which makes him a slave
In case your wondering how 7 5th level Thieves managed to get the better of 12 7th level Fighters? the answer is they didn't outfight them, they outsmarted them. Pretty good thinking for mere Thieves
They did this by arranging for 12 crooks they hate to do 7 muggings, the naive 4 year old send 10 of his guards to intervene, 5 of the 7 slave snatchers distracted the other 2 guards whilst the other 2 slave snatchers grabbed the 4 year old and used their knowledge of the cities back-alleys, alleyways, shortcuts, thorough-fares and backstreets to lose the guards