No, your statement about why the hamza was removed from "Ibn Al-Waleed" is incorrect.
The hamza (specifically, hamzat al-wasl or the connecting hamza) in "Ibn" (ابن) is omitted when it falls between two proper nouns, where the second noun is the father of the first.
In "Ibn Al-Waleed" (ابن الوليد), Al-Waleed (الوليد) is the father of Ibn (the son). So, the hamza is indeed dropped.
However, your statement: "حذفت الهمزة لانها وقعت بين اسمين ثانيهما اب للاول" (The hamza was removed because it fell between two names, the second of which is the father of the first) is describing the rule correctly.
The confusion might be in how you phrased "ثانيهما اب للاول" (the second of which is the father of the first). This is precisely why the hamza is dropped.
In summary: The hamza in "Ibn" is removed in "Ibn Al-Waleed" because "Al-Waleed" is the father of "Ibn". Your reasoning for the removal is correct, even if your initial sentence might have been interpreted as saying the reasoning itself was flawed.
اذا كان لديك إجابة افضل او هناك خطأ في الإجابة علي سؤال قدوتي ابن الوليد حذفت الهمزة لانها وقعت بين اسمين ثانيهما اب للاول اترك تعليق فورآ.