I think that the answer to your question lies in the will of John Smythe of 1534.
Let's examine what we are being told.
He makes his son, William Smythe, executor of his will. If this is the William Smythe who is the offspring of John Smythe and Alice Townhende then he is appointing a 2 year old child to be his executor. Most unlikely.
If however this John smythe was born about 1470 it is entirely reasonable to suppose that he has decided to make a will because he knows that he is about 64 years old and dying. that he does die is evidenced in that the will was proved in 1535 by his son, William Smythe.
He also has a daughter who is referred to as Agnes Smythe indicating that she is unmarried. He also requires that Agnes be given a third of his whole goods and this to be overseen by four credable neighbours. To be overseen by four neighbours indicates that he is not dwelling within a built up area and we can assume that he is a farmer. The only farming activity near Halifax will have been sheep for their fleeces to be sold in Halifax market. In these circumstances his will writer would have pointed out the need for his neighbours to ensure that sheep and land were fairly apportioned. His neighbouring farmers would be familiar with the stock and land quality and would be the best persons to carry out this duty.
There is no provision for his wife and we can be sure that she died before 1534. We don't know her name but if it was Alice or he had a sister called Alice Smythe then the will writer would want to make quite sure that there was no confusion as to who was to receive the 20 shillings. In that event he refers specifically to Alice Townhende, daughter of John Townhende.
This is clear evidence that he has a son, John Smythe, married to Alice Townhende.
The witness names are Interesting in that they are probably the four cerdable neighbours from whom John Smythe 1470 sought their future co-operation in the division of his property.
Now when we look at the submitted familysearch.com pedegree resource file for Alice Townhende this claims that she had four children. The first three are born in Farsley where a sheep farm would have been ideally situated in 16th century as this gave access to both Leeds and Bradford wool markets. Now we don't know much about John Townhende and his wife but if Alice were their only child then having John and Alice come to work on their farm (at Farsley ?) would ensure that their daughter would benefit from their labours.
That John no longer has any interest in working his fathers farm is evidenced by the greater part of John's estate being left to his son, William. William and Agnes have been running their father's farm and John has no need of his fathers support. Agnes would be a deserving partner because she was working the farm as sheperdess and acting as housekeeper since her mothers death. The division of property would ensure that they continued farming to their mutual advantage
I think that the fourth child, William Smith, born in Stratford-on-Avon, is a complete red herring adopted by someone compiling a family tree who included any child born to an Alice Townhende. Check out William Smith and you find that he is both married to Alice Townhende and has a mother called Alice Townhende.
I can only believe that there are two Alice Townhendes, one of which was born in Yorkshire and the other in Wiltshire. The Wiltshire Alice has a son called William born in 1532.
Hope this solves your problem.