Both "dissociate" and "disassociate" are defined as removing an association but is there a difference between the two? Does the "associate" part of "disassociate" imply a stronger former connection missing in "dissociate?"
OED says disassociate dates from 1603, and dissociate from 1623, so neither is meaningfully "the original". They're basically the same word, but if you believe this NGram dissociate is used more commonly by a factor of about 4:1 in total.
Many instances of disassociate will in any case be for the specialised chemical sense (compounds breaking down into atoms, ions, etc.) which only applies to that form, so for OP's meaning the usage figures are even more skewed.
Merriam-Webster's dictionary of English usage implies that apart from where that difference in meaning applies, you should probably prefer the shorter word - partly because it is shorter, and partly because it's the more common form. There are no other considerations, or differences in use or nuance.