It might have something to do with some nuances in terms of possession.
In 站在我旁边的陌生人偷了我的钱包, clearly a stranger is just a random person, you cannot say 我的陌生人. So this one is correct.
In 躺在我旁边的狗伸了一个懒腰, if this dog belongs to you, i. e. it's your only dog（我的狗）, the sentence is wrong. However, if you have no or several dogs, then there's nothing to find fault with in this example;
In 坐在我旁边的母亲问我今天怎么样, if there were 坐在我旁边的母亲 then there must be 没坐在我旁边的母亲, which is impossible as you can only have one mother;
And lastly, in your case "坐在我的旁边的朋友", it's obvious that the main emphasis is not that this friend of yours sits next to you, but the friend who sits next to you. You don't intend to emphasize: 这个朋友坐在我旁边，还有一些朋友没坐在我旁边. That's why I suggested that you move the subject forward and make “坐在我旁边” an action instead of letting it function as a modifier. （我的）朋友坐在我旁边，问我……