Here, "lovingly" is not modifying "apart". Instead it is modifying "prising". "Prising" is not a word I'm familiar with, but according to Dictionary.com when used as a verb it is a form of "pry". Additionally, the "them" in the phrase refers to "his wrists" from earlier in the sentence.
Thus, I will start with this phrase:
Prising his wrists
Alone this would be a pretty weird thing to say, but there are some additional adverbs to add clarity! The phrase as a whole follows the form "[Verb]-ing [noun phrase] [adverb(s)]", which I can't really put a name to but is fairly common. Lets add the most useful adverb:
Prising his wrists apart
"Prising apart" describes a clear and distinct concept from just "prising", so it is very important for actually understanding the sentence. However, the other adverbs don't modify "apart" they modify "prising" and thus can be considered independently of "apart":
Prising his wrists slowly
You don't seem to have any difficulty with this part, there's no contradiction between "prising" and "slowly". However, the other adverb can also be considered independently:
Prising his wrists lovingly
This phrase does end up being weird, "prying" and "lovingly" seem like a weird pairing, but grammatically it's fine. "Lovingly" also has a modifier that helps:
Prising his wrists almost lovingly
With this, the prising is explicitly not loving, but instead is similar to being loving. If "slowly" is included as well then there's even more detail:
Prising his wrists slowly, almost lovingly
Pairing two modifiers like "X, almost Y" in this way carries an implication that the two are related. Specifically it would most closely be interpreted as "done so slowly that it seemed to be done lovingly".
The way the words connect to each other can be made a bit clearer by changing the word order. This phrase has the same meaning as the original:
Slowly, almost lovingly prising his wrists apart
TL;DR: "Lovingly" modifies "prising", not "apart".