Is there any instance of part of a country successfully seceding and then unifying with a neighbouring country in the last century?

Hong Kong was, for nearly 100 years, a British Territory administered by the British government, originally during the Opium wars, when China was still under the rule of the Manchurian Qing dynasty, multiple regime changes ahead of the current People's Republic of China.

In 1997, the formal lease for the region expired, and a negotiated reunification with the people's republic of china was negotiated, and while there was no explicit threat of violence or anything, it was done with quite a lot of apprehension by the citizens of the city, and with the geopolitical backdrop of "if the Chinese wanted to take it, there wasn't much the British could realistically do about it, and the expiration of the lease pretty much had international law in China's favor". For the last 20 odd years, the territory has been ruled under the "One country, two systems" uneasy truce, and had done so relatively stably.

Obviously, the recent political crsis has made it unclear how stably and smoothly reintegration of Hong Kong into China has gone, but I know of no observers who expect anything like Hong Kong independence or a return of the region to the United Kingdom to even be an imaginable prospect.

The Saarland a part of France after the 2nd world war and voted to join Germany in 1955. It became a federal state of Germany in 1957.

Vietnam possibly.

is there any precedent for groups fighting to leave the country they inhabit solely as to join a neighbouring country, successfully, in the last century or so?

A movement was formed which rebelled against a colonial power (France) and succeeded by a combination of violence and political activity. This resulted in the formation of North Vietnam and South Vietnam. The south reneged on an agreement that formed part of the settlement and this led directly to the war which the US became mired in. This involved both an invasion from North Vietnamese forces and Southern Vietnamese rebels.

This ended with the reunification of Vietnam.

So you have a partition of a country, a civil war and invasion and finally a reunification. In this case the Southern rebels fought to join the neighboring North Vietnam (and did). Seems to match your requirements.

The most recent event of such kind is Autonomous Republic of Crimea, which seceded from Ukraine in 2014 and then voted to join Russian Federation in 2014 Crimean status referendum.

There are a lot of qualifications to your question that make a lot of the answers slightly miss the premises. I would argue that there is a systematic reason for the discrepance. If a group of secessionists wants to leave one country to join another, this by definition adds a third party to the conflict. It can never be a fight between the country holding the territory and the people wanting to leave, but must always include a positioning of the country they want to join. In fact, most of the time the "receiving" country will take an active part. And the military might of the two countries involved will be much more of a deciding factor than the secessionist fighters themselves could hope to be.

In that sense, here is another example that does not quite fit:

In 1918, both Azerbaijan and Armenia declared independence from the Russian Empire. Both countries claimed the Nagorno-Karabakh region for themselves. In August 1919 both countries signed a "provisonal treaty" that accepted Aseri sovereignity of the region under the rules of a partial autonomy. After several more rounds of conflict, in 1923 Nagorno-Karabakh was finally declared an Autonomous Oblast of the Azerbaijan Soviet Socialist Republic.

After 1985, the Armenians living in the region started to rebel again against the Azerbaijan rule. Until the end of the Soviet Union, this remained a more or less small scale uprising, but in 1992 escalated to a war between the two countries.

In 1989 the Armenian Supreme Soviet had declared Nagorno-Karabakh to be a part of Armenia. In 1991 Nagorno-Karabakh declared itself independent. In the years of war 1992-94, it were the Azerbaijan and Armenian armies, with the help of mercenaries on both sides, that actually fought. Since the truce of 1994 the Republic of Artsakh maintains it is an independent country, despite its ability to rule being always dependent on the presence of Armenian forces and assistance from the Armenian government. Since the 2020 war, when Artsakh lost one third of its territory, Russian peacekeeping forces (yes, in this case I think they can be called such) are another part of the equation.

So, was there ever a true movement of the people to join Armenia, or was it the Armenian government hiding their annexation intent behind so-called freedom fighters? Was the Nagorno-Karabakh independence ever a real aim, or only a disguise? Was it, in any sense of the word, ever part of Armenia? The answers obviously depend on which side you ask.

Not an example of a "violent" secession, but I think this perfectly captures the title question.

Hatay Province of modern Turkey seceded from Syria and on 29 June 1939, following a referendum became a Turkish province.

There are some good examples following the dissolution of Austria-Hungary;

In 1918, the Kingdom of Croatia-Slavonia proclaimed independence, merged with the newly constituted State of Slovenes, Croats and Serbs and then asked to join Serbia and Montenegro to form the Kingdom of Serbs, Croats and Slovenes.

Similarly, Banat, Bačka and Baranja declared independence and joined the Kingdom of Serbia.

Note that Czechoslovakia was different, Masaryk & comp. operated from (and achieved recognition of Czechoslovakia by the WWI victors) outside of the legal structures of Austria-Hungary.

There are other examples, but less clear cut (if the region was already occupied by the other country's army), e.g. the Republic of Central Lithuania joining Poland, quite a parable to this century Crimea; or if the end result was less than pleasant, e.g. the West Ukrainian People's Republic that joined the Ukrainian People's Republic only to be later overun by the Bolsheviks and included in the Soviet Ukraine.

Not A-H related, but in the same historical period Bessarabia declared independence from Russia and after some time joined Romania.

The Greater Poland Uprising (1918-1919) fits your criteria. The Poles in the Greater Poland region fought German rulers to unify with the newly created Second Polish Republic. Although it is a bit of a stretch. Earlier the entire Poland was occupied by Germany/Austria/Russia, and most of it regained independence. It could be argued that the uprising was just the continuation of that process.

Kashmir might be the biggest example, if you are willing to accept "de facto control" rather than "international recognition". Parts of Kashmir are currently de facto part of Pakistan, with the border being the "Line of Control". Here a region that had been part of India, broke away and joined a neighbour, although international recognition awaits a more comprehensive agreement between India and Pakistan.

Other examples (harvested from Wikipedia's List of border changes) I'm mostly looking at post WW2, as the period before 1945 is too chaotic.

1947 The Dodecanese and Rhodes seceded from Italy and merge with Greece.

May 1961, The Northern part of "British Cameroons" seceded from the colony and became part of Nigeria. "British Cameroons continued for another 6 months before the remainder of the country merged with Cameroon.

Feb 1994 Walvis Bay and the Penguin Islands seceded from South Africa and merge with Namibia There have been other small transfers of territory, between Poland and the USSR, for example. Like Walvis bay, these have generally not involved violence.

Crimea (ongoing) While this is obviously part of an ongoing war, Russian control in Crimea is not being seriously challenged at the moment and so Crimea has de-facto seceded and merged with Russia.