What does the verb + 到 structure mean here? 他决定先躲到奶奶家...
What is the function of 到 here? Does it indicate successful completion, direction, or something else?
到 in [V + 到] can be a result complement

From https://resources.allsetlearning.com/chinese/grammar/result_complement


Forming the result complement


Result complements form verbal compounds that behave exactly the same as normal verbs. The compound is formed by a verb plus another verb or an adjective:
Result complement examples


Verb:听


result complement:听到


(听 alone means 'to listen', but 听到 means 'to hear'.

Edit:
However, since it is followed by a location/ destination, the 到 in 躲到 is different from the 到 in 听到--  it is not a result compliment but the preposition 'to/ into'
Example:
'躲' = to hide. e.g. 快躲 (hurry and hide)
'躲到 + location' = hide into location/  destination. e.g. 躲到小红帽奶奶家(里) (hide into Little Red Riding Hood's grandma's home)
Summary:

到 here means 'into' because 小红帽奶奶家 is a location/ destination to hide into. If it was 躲到美国 then 到 would mean 'to' because 美国 is a location/ destination to get to

到 in 听到谣言 is a result complement that indicates the verb is completed  because 谣言 is an object to be heard

在 in 躲在小红帽奶奶家 (hide at Little Red Riding Hood's grandma's home) means 'at' which is also a preposition because 小红帽奶奶家 is a location to hide at