Convincing a school to let them in for 3 months when you've got winter break in July is going to be tough. It would be smack in the middle of the year (think of it like putting your child into a North American school in november and taking them out by february. If you're serious about schools you'd have had to sign up at least 6 months ago -- by now people will have already signed to start in March, so finding spots for all four could be very difficult, especially if you have any desire to send them all to the same school. Your best hope is if thanks to inflation a lot of families withdraw their kids mid-year because they can't pay the tuition, but really you're looking for 4 vacant spots and only for a few months -- there are not a lot of schools that will be open to this idea. Do a search on this forum for schools in Belgrano and some private options will come up. Public there's only a couple here you'd even think to send them to and you won't be able to anyway since the kids won't have DNIs.
You might just want to sign them up for a club instead -- there are plenty in town and in zona norte. Did you just come off the 4mos in Mexico? If so and they are losing schooling time your best bet for education would probably be to hire a private tutor, though if moves like this are regular I presume you already have one (or are doing the tutoring yourself). Your kids will probably also be thrown a bit by the Spanish here (if they aren't, you may be!) It's quite different than Mexican spanish and certainly more rapidly paced.