But it depends on the reliability of the sister in law. I wouldn't hesitate to let my brother take my kids out, I know that they would be safe, that if anything happened DB would be more than capable of coping, that he can handle nappy changes or accidents of that nature, etc etc.
MY husband's sister on the other hand, no way. She panics when the kids so much as cough. She is completely incapable of taking them anywhere. She wouldn't be able to handle the eldest alone, he has complete control over her. DS2 is a runner and if he took off while they were walking down the street or something, she just wouldn't be able to handle it. She needs supervising herself when they are around - she plays really nicely with them, but has absolutely no control over them or authority, and wouldn't know what to do in a toilet accident, or any kind of emergency. I don't think she would know what to do on her own in any kind of emergency - she has been so mollycoddled and smothered by her parents; she doesn't know how to use the washing machine, or cook, or anything.
So I wouldn't be agreeing to my SIL taking my son out in the buggy at all, unless I knew that FIL/MIL was there too. Last time we all went out, SIL pushed the buggy, but couldn't work out how to get it up the kerb and so just left the buggy in the gutter and asked someone else to do it. It's not her fault, she's been so smothered by her mother that I'm amazed she can go to the toilet by herself - that sounds bitchier than it's meant.
Anyway, I think it utterly depends on the capability of the SIL, and also the relationship between OP and her SIL - there are people in my family that I won't have in my house, let alone let them take my child out, so it really does depend on other factors other than "she's his auntie, what's the problem".