If so, is there a difference in meaning between "You always can trust me" and "You can always trust me"? I believe there is, because in the second sentence, "always" modifies "trust", unlike in the first sentence.
You asked if there is a difference in meaning between them. But then you say the position of "always" is the difference - that is not a difference in meaning.
According to Cambridge: Adverbs and adverb phrases: position,
The mid position is between the subject and the main verb ... Where there is more than one verb, mid position means after the first auxiliary verb or after a modal verb.
The government has occasionally been forced to change its mind. (after the first auxiliary verb)
You can definitely never predict what will happen. (after a modal verb)
We mightn’t ever have met. (after the modal verb and before the auxiliary verb)
Adverbs usually come after the main verb be, except in emphatic clauses ... When be is emphasised, the adverb comes before the verb
- Why should I have gone to see Madonna? I never was a fan of hers. (emphatic)
The most common word order is modal + adverb + verb. While the construction "You always can trust me" may be grammatical, it is not common usage. So, this form is not wrong, but it sure is rarely used (see the comments in the linked post).