«Мои дети ходят в школу» means ”My children attend school”. This is simply the way you say “to go to school” in Russian.
If you want to stress the fact that they walk (on foot), you can say «Мои дети ходят в школу пешком.»
If you want to have a continuous feeling to your sentence (as if they are en route to the school), your best option is «Мои дети (сейчас) идут в школу».
The point here is that ходить supposedly means "to go by foot", which in English means "to walk", so that ходить в пешком would literally mean "to go by foot on foot".
In one exercise, people were marked wrong for using идти instead of ехать because the distance was inferentially great, so that walking would not be likely. Duo was being very precise there.
But here, where ходить seems to be a multi-directional version of идти, we find that "on foot" isn't relevant. There seems to be a logic problem there.
My kids walk to school was added, actually.
A bit a clarification: the sentence in the title does not suggest that children are walking to school instead of going there by bus (unless they travel to school that is, like, in another state). Ходить and идти are commonly used for your trips within town—to places like work, school, a store, a museum or attending some classes and events, all regardless of how exactly you get there.
In this sense, the use of идти/ходить with школа, работа or концерт will not be the same as with a random place name (to be on the safe side: I mean a concert somewhere nearby).
идти is also used when talking about public transportation and routes (in fact, the common end of line announcement in Moscow Metro ends with "Поезд дальше не идёт, просьба выйти из вагона.").
The go vs walk aspect seems to be confusing for English speakers and as a bilingual person (english/polish) I can see that English is lacking a way to express the same meaning, using "go" means to move to a place without specifying the mode of transport, just like the Russian (and analogical Polish version) ходить. The word is used colloquially for using any mode of transport within a town/city to get somewhere (a school or work or café usually is within a close distance), the only issue in understanding is that the word equivalent to "going" came about from a word meaning "to walk" and is still also used in that meaning. Context is required to differentiate, in which way the word ходить is used, for example ("to school", a place close by, known as an everyday occurrence = attending school).
However, there is a difference in this case: "are going" would be «идут»; «ходят» describes a habitual action, not something that is happening right now. I'm not sure what's the grammar rule on this, but as a Russian native, I'd say you cannot translate it as "my children are walking to school".
Later edit: look up verbs of motion, unidirectional vs. multidirectional.
This is actually incorrect in two ways:
1) The ходят here implies a permanent action, so you can't translate it as something that's happening right now. For that you could say идут.
2) Ходить here does not imply walking. For that you would want to use ходить пешком / идти пешком.
Therefore, your sentence in Russian would be: Да, мои дети идут в школу пешком.