Would they swim on the same day as their Zayde’s levayah? While they are not obligated to fast, think about the destruction of the temple, etc., I believe most people don’t give their kids candy or meat on the 17th of Tammuz, and stick to basic, simple foods. There is a value in getting kids familiar with the mitzvot that they will later have to undertake. The 17th of Tammuz sets the tone for the Three Weeks, and maybe there are alternatives to taking kids to the pool.
Unless they are VERY young, the day is VERY hot, and they have no alternative to keeping cool, I would not allow my kids to go swimming today. And in the aforementioned dire case, I would say sprinklers are enough to cool them off,and even that, feels wrong to me, if there are other ways to handle the heat.
The Debritziner in the Beer Moshe, cheleck Gimmel Siman ayin Zayin, discusses this very shayla. I dont know if external link to hebrewbooks page of this sefer will be allowed, here it is on the chance that it will be permitted…. http://www.hebrewbooks.org/pdfpager.aspx?req=888&st=&pgnum=116
If the link is not allowed, here is the summary. For his full teshuva, see the sefer.