Adjective describing a person who has lots of children, not "fertile"

Merriam-Webster gives prolific:

1 : producing young or fruit especially freely : fruitful

The source is Latin proles meaning "offspring".

fecund:

producing or able to produce many babies, young animals, or plants
- Merriam-Webster

Your question seems not to be about a general family situation but about the technical situation with data structures in computer science. In the latter case, a binary tree is for internal nodes with two children, ternary for three. The generalization is then

multiary

for many children. Other, similar ways of saying this are _n- ary (for an arbitrary number not necessarily many) or var-ary for a possibly changing number of children. All of these are somewhat ... let's say non-classical, but are acceptable within the technical community.

Given what OP has described in the comments, I think branching node would be ideal. We're referring to a node which has branches. We could modify it to highly branching node to clarify we're specifically talking about nodes with a lot of branches.