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I would tell her directly to lay off, and that if my child needs correction, I will be the one to do it. She is way over stepping the line here.

If you can, you should get a place of your own. It's tough to raise a child with such family dynamics.

Can you & SIL write up a list of house rules & post them and apply to all kids?

I would just try to mention it to her. I have to admit that I used to reprimand my ex-roomate's DD when she was misbehaving, but I didn't know it bothered her... until my aunt mentioned it to me. (so I stopped... mostly. lol) She might not even know it bugs you.. or she might not even realize she's doing it. If she insists on keeping it up, I would just wait for SIL to reprimand your DD, then just casually say 'oh, she's fine' or, if she is actually doing something, tell SIL that you would rather her point out the problem to you instead of reprimanding DD...

Is she disciplining your child because she thinks she is going to hurt her child? "Your cousin has a mommy, don't pick her up" leads me to believe that there is more to the story. You don't say how old your niece is but maybe your daughter has dropped her cousin before and that's why your SIL is so protective? I have a relative that doesn't like to correct her children (she doesn't see anything wrong with the way they behave apparently) and when her children's behavior is affecting my children's safety or they are abusing my children's things, yes, I will correct them myself if I don't see her doing anything about it. Her idea of correcting her children is saying, "Bob-by...?" and she give them a look. Then they go back to doing what they were doing and she sighs.
Maybe you need to have an honest conversation about this with her since you have to live under the same roof. Be nice about it. See what happens...

Does your daughter require the discipline?????? If you see that a correction is in order try to beat her to the punch. If she is excessive about it, I would not make a big deal about it but I would discuss it.

Have you told your SIL straight up, "I would appreciate it if you would leave the disciplining of MY child to ME."

My SIL has done this to me, and I finally just had enough and snapped at her one day. i said.. 'hes my child, Ill do the diciplining'. She never said anything else after that. lol.

stop leaving her there without you being right there. then you get to be the disciplinarian. the kids will never be friends if this continues.

Just tell her that you appreciate her trying to keep the peace, but you and your husband need to do the reprimanding when you are there. If you aren't there, is she allowed to reprimand? If so, then just tell her that when you aren' there, she is welcome to continue the consistency of rules. With a family crisis, your daughter needs to know that you and dad are still in charge.

Updated

Just tell her that you appreciate her trying to keep the peace, but you and your husband need to do the reprimanding when you are there. If you aren't there, is she allowed to reprimand? If so, then just tell her that when you aren' there, she is welcome to continue the consistency of rules. With a family crisis, your daughter needs to know that you and dad are still in charge.

Dont keep being quiet. EVERY single time she does it say "MY child, I'LL deal with it since I'm here" and then deal with it. Say it over and over, keep it very brief dont give explanations, dont try to be polite, dont phrase it differently every time. Repetition works best. Dont waste time with your SIL when your daughter needs disciplining, its better to deal with small children right away (I could see myself getting so upset with SIL that I ignore child's bad behavior) Your daughter will quickly learn to ignore her aunt and look at you. Also dont be shy about saying "Your daughter cries every time her cousin looks at her, is she like that with other children, Are you worried about her social skills?"

Simple if you don't want her to discipline your child not bring your child over there.

Edited: it would have been helpful if you originally said you all live together. I think there is more going on here. You said "your cousin has a mommy don pick her up" you might not alway think your daughters behavior is wrong but your sil might be afraid that her helpfulness is going to cause harm to her child.