It has to be something strange about the cell phone. It should connect to your router but it is hard to say why. Phones have few diagnostic tools to help.....you click a icon and it just magically works all the time
If your computer is using wifi to talk to the router it will be difficult to use it as a hotspot. If it was connected via ethernet then it is easy but that is pretty much what a AP is.
It really should not matter the phone may have issues connecting to the hotspot. It all depends why the phone is being stubborn. I know mine I have just deleted all the networks and told it to find a new one and it connected right up even though 10 seconds before it pretended the network did not exist.