Position rule: the big structural difference
一点 is a post-adjective modifier. It follows the adjective directly: 便宜一点 (a little cheaper), 大一点 (a little bigger). 有点 is a pre-adjective modifier. It precedes the adjective: 有点累 (a little tired), 有点贵 (a little expensive). Swapping the position is ungrammatical: 一点贵 and 有点便宜 both sound wrong to native ears. Train the position first; the nuance comes later.
这件大一点,但是那件有点紧。
Zhè jiàn dà yìdiǎn, dànshì nà jiàn yǒudiǎn jǐn.
This one is a bit bigger, but that one is a bit tight.
Negative tone on 有点
有点 always implies the speaker is mildly dissatisfied. 有点累 suggests I am tired and wish I were not. 有点贵 suggests the price exceeds what I wanted to pay. You cannot say 有点漂亮 to mean "a little bit pretty" as a compliment; the sentence would imply the person or object is pretty in a way the speaker finds uncomfortable. For neutral or positive "a little", use other structures like 还不错 (not bad) or 挺X的 (pretty X).
一点 is comparative or suggestive
一点 frames the adjective as a comparison or a request. 便宜一点 (a bit cheaper) implies "cheaper than something, or cheaper than now". This makes it the standard bargaining phrase: 便宜一点吧 (make it a little cheaper, please). You can add 再 for "even more": 再便宜一点 (even a little cheaper). With 比 comparisons, 一点 is the default quantifier: 他比我高一点 (he is a little taller than me).
能不能再便宜一点?
Néng bu néng zài piányi yìdiǎn?
Can you make it a little cheaper?
The 有一点点 emphasis trick
To emphasize how slight the complaint is, native speakers double the 点 or add degree words: 有一点点累 (just a tiny bit tired), 稍微有点贵 (slightly a bit expensive). To soften 一点 in requests, add 吧: 便宜一点吧 is softer than bare 便宜一点. The 吧 converts a command into a suggestion.