Hi Dee; Just want to make sure that you're aware that March in Greece is not like March in Caribbean, temps much more like mid-USA. March 1-30 ave temp is 52°F, so early March likely below 50°, and it's still in shower-y season. Just keep that in mind, and forget packing swimsuits.
On Santorini In March, you may be best off staying in Fira town or Firostephani (north end of Fira Town) because that is where the most things will be open. No need to pay for a pool hotel outside of swim-season. To get best suggestions from the Santorini experts on this forum, give us your desired budget range per night in Euros (here's the good Instant conversion website - http://www.xe.com/currencyconverter/ . Also, do you want a unit w 2 BR? or a sort of 1 BR-Studio unit? (1 BR and LR w 2 daybeds). With children that age, I'd think that 2 nights in Santorini would be enough ... not as much for them to do at that season -- it is mainly the famous Caldera View, and kids get bored quickly with views. The Akrotiri escavation really is most interesting for adults. You could consider Ancient Thira, as a hiking challenge.
About Delphi, If u fly back from Santorini, u can rent car right at airport and easily drive to Delphi in about 3 hours. This website http://www.viamichelin.com shows best route, time, cost in tolls & gas -- just put in ATH Airport GReece as start-point, then DELPHI Greece as destination. HOWEVER, until April 1 both the site & the Museum close at 3 PM ... so in order to do it in one day, you'd really have to leave the ATH area by 8 AM. A more relaxed approach would be to arrive ATH airport in Afternoon, drive up before dark, take a hotel for the night, then go to site & Museum at 8:30 in AM. Hotel PAN has marvelous balcony views down mountainside to the sea from its rooms at the back.
For many, Delphi is an absolute MUST, but if it's just one option you are weighing , consider instead doing NAFPLIO for 2-3 nights. Kids Loove this Old Town (on a peninsula, feels llike an island) -- because it has so much to explore, in town & nearby. Castle in Harbor, Castle ramparts atop the town, and behind town, a huge fortress (Palamidi) on a Gibraltar-size "rock"... 999 steps (tip: u can drive up the back way and walk DOWN). The town square is paved in MARBLE, the small museum there is Very well organized, with video interaction ... there's a local playground. If the weather suddenly turns sunny & mild, there's Tolo beach 10 minutes out of town where kids can caper on the sand. AND if you drive to Nafplio from ATH airport (2+ hours on v. modern divided highway), you can visit other local ancient sites ... Tiryns fortress, Epidaurus, etc. This fab noncommercial Website http://www.visitnafplio.com/visitnafplio.com/Home.html shows lovely visuals ... this Map (click to enlarge) -- http://www.esperides.gr/images/peloponissos_esperides.jpg -- shows exactly how to get there. A PLUS: on way to or from, right off main highway near Corinth Canal... there's NEMEA, an ancient Games Site (runner-up to Olympia). Ruins, AND restored arena, where u can use ancient start-blocks for racing. Its a quick stop, and kids love it.
Finally, do try to stay at least 1 day in Athens, to take the kids up on the Acropolis at least... they'll remember it forever.