"Hit/clout/slap round the head" is a UK idiom. It doesn't imply once or more than once.
Examples from the BNC:
"clouted it very hard round the head with his stick"; "clouting him round the head"; "getting a tap round the head"; "who beats you round the head"; "Because you can't wallop them round the head can you?" and so on.
There's a more specific form "round the ear": this is nearly always "clip round the ear" (17 times in the BNC) but also "smack", "clout" and "belt" (6 instances in total). ("Clip" meaning a blow only occurs in this one phrase, as far as I know, but as a verb it can be used to mean "make an accidental, glancing contact", as "I clipped it with my mirror as I went past".)
Quite why we say "round" is not clear: it is certainly an aphetic form of the preposition "around". It doesn't seem to occur with other body parts than heads and ears (there are a few possible instances in the BNC, but they all might be interpreted as a literal "around"). It doesn't seem to imply any particular part of the head, or multiple blows "all round the head", as one might have supposed.
The cat above is peering/looking/peeking around a corner or a bookcase, or whatever this non-transparent object is. She would like the rays of light from her target to reach her eyes along a curved line, going around the corner; but that isn't possible, so she has to move her head partly "around" the corner, or bend her body around the corner, to see what's going on. The cat in your story is doing the same around someone's legs. As Aedia says above, it is the same as peering from behind something, peering while you're mostly standing behind something.
Looking around an open space, like looking around a room, is different: then your head or body is rotating around an axis, so that you can look in several directions successively. There is no blocking object.
P.S. To everyone: I apologize for the cheap cute-cat trick, but a picture was really the easiest way to show what's going on, and this one was on the first page in Google Images, and, well, it is a cute cat.
P.P.S. This one is even more impressive:
P.P.P.S. Oh, I really couldn't resist this one, I'm sorry...
Best Answer
Short answer
Yes, you can.
Modern grammars such as the Oxford Modern English Grammar show there to be a preposition, not an adverb. The preposition in cannot take adverbs or adverb phrases as Complements. It can take other preposition phrases as Complements. For this reason there is no problem using the word there after the preposition in.
When we use there with a stative verb, it has a general meaning of at that place. If you want to say something like in and at that place, you can say in there.
Full answer
In modern grammars such as Oxford Modern English Grammar (2011) or The Cambridge Grammar of the English Language (2002), prepositions are a class of word like verbs, nouns, adjectives and so forth which have specific properties. Although taking noun phrases as Complements is a common feature of typical prepositions, this is not a necessary feature of this class of word. So many prepositions like the word out often occur without a following noun phrase:
This is similar to how, although many verbs take noun phrases as Direct Objects, this is not a mandatory feature of verbs. These developments regarding prepositions, have not filtered into dictionaries yet. This is likely to take many decades. Traditional grammars and modern dictionaries take words like out in the sentence above to be an adverb because it doesn't have a following noun phrase.
According to linguists such as Jespersen and Emonds and modern grammars such as CamGEL and OMEG, the word there is a preposition (some linguists think of it as a pro-preposition). It passes every test for preposition-hood and none of the tests for being an adverb.
It can appear as a Locative Complement of the verb BE:
It can be modified by the specialised adverb right, which can premodify many preposition phrases, but cannot premodify adverbs in standard English:
It can be premodified by the specialised adverb straight, which can premodify many preposition phrases, but cannot modify adverbs in standard English:
Preposition phrases can freely postmodify nouns, adverbs usually cannot:
We can usually use the adverb very to modify adverbs. We can't use it to modify prepositions or preposition phrases such as there:
All of this information shows that there is a preposition and not an adverb.
The Original Poster's question
The original Poster says that prepositions cannot usually take adverbs as Complements. This is a good rule of thumb! But it might be better to think about prepositions in the same way we think about verbs. Some verbs don't take Complements. Some verbs only take noun phrases as Complements. Other verbs cannot take noun phrases as Complements, but only take preposition phrases and so forth.
The preposition until can take adverb phrases as Complements:
However, the preposition in cannot:
However, the preposition in can, of course, take preposition phrases as Complements:
For this reason we can use there as a Complement of the preposition in:
The word there means something like at that place when it is used with stative verbs. If you want to say something like at that place and in that place, you can just say in there.