A few things here:
I don't know what this is for, but if you're writing for a North American audience, we don't say 'handicapped children' -- it is more politically correct to say "children with special needs". This may be the case in the UK too but I wouldn't know.
When referring to children without handicaps, we would likely say "typical children" or "typically-developing children".
Regarding the phrase you're constructing: If you could give broader context for what you're talking about, that would help.
When talking about, for example, a classroom with mostly typical children, where you bring in a child with special needs, we would say the children with special needs are being "integrated" into the classroom. Whenever it involves a situation that was initially built for typical children, we typically talk about "integration" for children with special needs.
Other than that, I would need to better understand the context to help. But I wouldn't say "commingle".
ETA: "We allow. . . children to mix with each other." works. As well as just "We allow. . . children to mix."