I would say "make". It is often used with "feel" for many examples. Here are a few: "Did I make you feel stupid?" "You made me feel unwanted." "You make me feel like a child." "I don't want to make you feel unappreciated." If I use the word "have", an example would be to use "feelings" as a noun, rather that "to feel" as a verb: "I have a bad feeling about this." "I don't want you to have bad feelings about this." I don't think we would ever used "get" when it comes to the feels. :)

I agree entirely with Marlana's answer. It does occur to me, though, that you can use "have" with a present participle, as in You had me feeling all excited (This implies that it was only a temporary thing and is often used in a half-reproachful way.) I'm afraid as well I can't quite agree with your division between "have" and "get" - "have" in that sense is extremely rare in conversation and not that common in writing either. "Get someone to do something" is very indeterminate and covers everything from forcing them to successfully suggesting something.

"I'm trying to get you to feel good about this." get = persuade or help "I want you to have a feeling of ownership about this project." have = have (not really causative, sorry) "I want to make you feel valued." make you feel = give you a feeling of being (valued) If you make someone do something it implies force, but if you make someone feel something it does not, although like all feelings it might be hard to resist. "You make me feel so happy" "You make me feel whole." "You make me feel like maybe life is worthwhile after all." If you have someone do something for you it does imply they don't have much choice. "The teacher had her students do the assignment." - there will be consequences if they don't. "I'll ask John to bring some food" - John is probably a friend. He can say no. "I'll have John bring some food." - John is probably an employee. He can't say no. Perhaps it is an American thing. In British English "ask" or "request" are so different as to be almost opposite to "have" used in this way.

I was referring to 'have' as a causative verb and in this case it indicates you are requested or asked to do something: 'The teacher had the students do the assignment'.

Marlana's answer is very good, but I wanted to point out that it is not quite right that "-'have' to say that you've been requested to do sth". "have to" usually means you are required to do some thing. "I cannot go to a movie tonight, because my boss says I have to work late." It is also used when I am unable do something because I have a commitment to do something else: "I cannot go to the beach on Sunday because I have to help my friend move to a new apartment."