Let's look at the actual definitions of force in the dictionary you referenced:
1 [often passive] to make somebody do something that they do not
want to do
This definition refers to a force against the will of another person.
*The president was forced into resignation. (Against his will)*
- Resignation is a noun, used as the object of the preposition into.
The President was forced into resigning. (Against his will)
- Resigning is a noun form (gerund) of the verb resign, used as the object of the preposition into.
The President was forced to resign. (Against his will)
- To resign is the infinitive of resign, used as an adverb.
All three sentences can have the same meaning:
The President didn't want to resign, but something overcame his will. The passive voice "was forced" is often the signal of this meaning. Just about any kind of adverb can modify was forced, and action adverbs work particularly well, because people can be forced to do things against their will.
The second definition of force shifts the focus a little bit:
2 to use physical strength to move somebody/something into a
Now the definition refers to a strong person (or thing) moving another person (or thing) into a position:
Bad weather forced the plane to land.
- Bad weather is the strong thing, plane is the thing being forced, and "to land" is the position.
Ill health forced him into early retirement.
- Ill health is the strong thing, him is the person being forced, and retirement is the position.
The first sentence is a thing forcing another thing, so there is no "will" involved. The second sentence is a thing forcing a person, so maybe the meaning of forced is a combination of the first two definitions. Either way, you can use the same three methods to modify forced:
Ill health forced him into early retirement. (Against his will?)
- Retirement is a noun, used as the object of the preposition into.
Ill health forced him into retiring early. (Against his will?)
- Retiring is a noun, used as the object of the preposition into.
Ill health forced him to retire early. (Against his will?)
- To retire is the infinitive of retire, used as an adverb.