Of American-English origin, the phrase between a rock and a hard place, and its variants, mean: faced with two equally difficult alternatives; in a dilemma.
—Synonyms: between the devil and the deep blue sea – French entre le marteau et l’enclume (i.e., between the sledgehammer and the anvil).

The phrase between a rock and a hard place occurs, for example, in ‘I’m quite fearful’: workers and employers on growing inflation, by Richard Partington, economics correspondent, published in The Guardian (London and Manchester, England) of Tuesday 15^th February 2022:

Matthew Tovey, NHS nurse, south Wales
“It seems to me like I’m just working to be able to cover the bills,” said Matthew Tovey. The 30-year-old from Merthyr Tydfil, south Wales, said his pay had not risen above inflation for a decade under the Conservatives’ austerity drive.
[…]
“It feels like if I’ve worked hard and gone into a profession to better myself, and I’m in this position, how the hell are other people coping?
“It impacts on your mental health, there’s nowhere to turn. You’re caught between a rock and a hard place and you wonder, when are we going to have a break?”

The earliest occurrences of the phrase between a rock and a hard place and variants that I have found are as follows, in chronological order:

1-: From one of the unconnected paragraphs making up the column Locals and Personals, published in The Poteau Weekly Sun (Poteau, Oklahoma, USA) of Thursday 1^st October 1914:

As an example of fine distinctions, a party of men were discussing the present situation of the German army, this week. One remarked that the Germans were between the devil and the deep sea; while another corrected him by saying that the Germans were between the upper and nether mill stone The third man whose name is Pillgreen, and who works in the treasurer’s office, simply remarked that the Germans were between a rock and a hard place. Here’s hoping that all three versions are in the main correct, so as to end the war.

2-: From The Columbia Record (Columbia, South Carolina, USA) of Friday 13^th August 1915:

THEY’RE FUSSING OVER IN JAW-JAW
(Special to The Record)

Atlanta, Aug. 13.—Gov. Nat E. Harris must be finding himself today “between a hard place and a rock” if all the “pressure” that is being talked about is really being brought to bear on him for and against the inclusion of prohibition in the extra session call.

3-: From the Americus Times-Recorder (Americus, Georgia, USA) of Friday 13^th August 1915:

GOVERNOR HARRIS HAS PUZZLING ISSUE PRESENTED TO HIM
(Special to Times-Recorder.)

ATLANTA, Ga., Aug. 13.—Gov. Nat E. Harris must be finding himself today “between a hard place and a rock” if all the “pressure” that is being talked about is really being brought to bear on him for and opposing the inclusion of prohibition in the extra session call.

4-: From a letter to the Editor, by one A. E. Van Velsan, published in the Miami Daily Metropolis (Miami, Florida, USA) of Wednesday 18^th August 1915:

Mr. Editor, nobody sympathizes with the colored people in this controversy more than I do. The negro being of course nothing more than an innocent bystander is consequently in the greatest danger. He is between a hard place and a rock and in order to protect him from any further damage it is incumbent upon the city council to take some action in this matter.

5-: From the caption to the following cartoon, published in The Alaska Daily Empire (Juneau, Alaska, USA) of Tuesday 5^th December 1916:

Fuller Bull Says:

COME ON WITH US!
NO! GUESS I’LL GO HOME!

A HENPECK with no place to go but home is between a hard place and a rock.

6-: From a letter that a certain Sergeant Jason C. Williams wrote to his family from “somewhere in France” on Saturday 9^th November 1918, published in The Mountainair Independent (Mountainair, New Mexico, USA) of Thursday 19^th December 1918:

Seeing from the papers, that we have the Central Power bunch between a rock and a hard place, I am afraid that the hard place will get harder than the rock if Fritz don’t wake up and get out while he is yet breathing.

7-: From The Gastonia Gazette (Gastonia, North Carolina, USA) of Wednesday 16^th July 1919:

GUBERNATORIAL GOSSIP.

Around the courthouse corridors and drug store fountains, they are beginning to talk of the coming gubernatorial campaign. Although a year off it is beginning to attract attention.
All of the three candidates have their supporters in Gaston county. It is impossible, of course, to say which is the strongest. Many Gaston county voters who do not know Bob Page well enough to sympathize with him, are finding themselves between a rock and a hard place, as one man put it, when it comes to Max Gardner and Cam Morrison. All admit that both are good men. One is a good friend to Gaston county on the east and the other belongs to the good Cleveland county regime which Gaston has always supported. One comes from the county of Mecklenburg which has never had political recognition, chiefly because of its own factional fights, and for that reason, deserves none, they say. The Cleveland county candidate comes from the section where politicians and office holders grow on trees, at [sic] it were. Enough patronage has gone that way, they say.