1
Be tactful with her: she has a rather special personality.
Be tactful with her: she has a rather peculiar personality.
Special often means important, valuable or different in a good way: ‘She’s a very special friend.’ It can also mean different from what is usual: ‘The school introduced special measures to help new students.’
Peculiar means strange or unusual and can have a negative meaning: ‘He has a peculiar way of speaking.’
In the purple sentence, special is possible, but peculiar expresses the intended negative meaning more clearly.
2
I’m very special with my clothes.
I’m very fussy about my clothes.
Use fussy about when someone is not easily satisfied with something: ‘He’s very fussy about food.’
Do not use special with or special for with this meaning.
See SPECIALLY