For a change, I agree with Trump. If you want to reduce illegal immigration, reduce incentives to do so. Having your kids become US citizens is a very strong incentive to illegally immigrate to US.
US would get much better immigrants by using merit-based approach to legal immigration - invite in educated, healthy, young couples that already speak English and could quickly assimilate and become productive. Instead of taking in the worst what other countries have to offer.
However, I don't think this could or should be accomplished via executive order.