You seem to exist in a very narrow minded realm of thought and aren't really opening your mindspace up to allow yourself to have some real insight into how these geopolitical manouvres really work.
It isn't in either Iran's or the US's interests to have another war in the Gulf, which will likely cost many lives and billions of dollars. If there is any "war" it will likely be a short exchanges of cruise missiles, warning shots and maybe some jetfighter confrontations in the air. Any such conflict would likely end very quickly at the negotiating table, with both sides wanting to quickly pipe down and avoid any further escalation. The UN and major world powers would get involved diplomatically and urge an urgent diffusing of conflict.
Also it isn't in the US's interest to spend potentially trillions of dollars and doom a sizeable number of its soldiers to death to perform any ground invasion of Iran; it isn't even in American interests to depose Iran's regime, which maintains stability over ISIS and is also a major Russian ally.
That said, if any such confrontation did happen, Israel would likely contribute intelligence to their American allies, but in terms of soldiers and conflict, the US would be able to handle it alone. Also Israel's military is primarily built for a defense of country itself, without any large navy that could travel the distance to make any difference over in Iran.
Furthermore, it is highly likely Iran would call upon its allies Hamas and Hezbollah to either jointly or separately attack Israel, so Israel would already be proccupied with self defense. Further to this, Iran would possibly launch long range missiles at Israeli territory in some sort of anti-American ally manouvre, in the same way that Saddam Hussein's Iraq shot missiles at Tel Aviv around the time of the Gulf War, as well as threatening Israel with WMDs.
If Israel sent half its military to help support American forces, even though it lacks the naval means to and would be of unnecessary additional value, requiring if anything complicated coordination between allies rather than just one military which is large and difficult enough to coordinate as it is, Israel would face an existential threat of annihilation or widespread destruction. It is actually further in US interests for Israel to stay put and defend itself as an important regional US ally.