The manual for the Korg DP-80 says to use a Korg PS-1 or DS-1 pedal, or the equivalent. Korg's website shows the
PS-1 and
PS-3 pedals as being currently available, as well as the
DS-1H pedal.
The PS-1 and PS-3 look like they're interchangeable, so I guess the only differences between them are color and the shape of the plug (the SP-1 has a straight plug; the SP-3 has a right-angle plug). They are foot switches, and are used to switch the damper/sustain function on or off. Foot switches can be latching/non-momentary or non-latching/momentary, meaning you can either click them on or off so you don't have to keep depressing them (latching/non-momentary), or they are off if you are not depressing them and on if you are depressing them (non-latching/momentary).
The DS-1H looks more like a piano damper pedal, which some people prefer-- unless they want a foot switch that can be latched on. I'm not sure whether there are any differences between the DS-1 and the DS-1H, but the DS-1H supports half-dampering. I don't think the DP-80 has half-dampering capability, but I suppose the DS-1H pedal will still work with it; you could contact Korg Support for clarification on that.
The manual for the Kurzweil SP2 says to use a Kurzweil CC-1, FS-1, or KP-1 pedal (or the equivalent). Kurzweil's website shows the
CC-1 and
KFP-1 pedals as being currently available; the
FS-1 has been discontinued. There are jacks for two pedals-- one for the CC-1, and the other for the FS-1/KP-1.
The KFP-1 and the discontinued FS-1 are similar in function to the Korg pedals described above.
The CC-1 is different-- it works like an expression pedal, meaning it can vary the volume, expression, or other "continuous" parameter from a minimum setting to a maximum setting.
Some people prefer to buy pedals and other accessories from the same company that made the keyboard, but you can sometimes save a little money by buying a third-party pedal. If you decide to do that, you might want to get pedals with polarity switches so you can change their polarities if necessary. You might want to talk with your two children to see if they have a strong preference between a latchable foot switch style or a piano pedal style. If they currently don't have any knowledge or experience about either type then they might not have a preference yet, but if you explain the differences and ask them to think about it then they might decide that they'd prefer one or the other.