BANGKOK, Thailand — As father-daughter dances go, there may be few more awkward in modern political history than the one being choreographed in Bangkok these days.

Thailand’s new Prime Minister Paetongtarn Shinawatra, 38, is the daughter of a coup-toppled, convicted, former international fugitive — and former prime minister — Thaksin Shinawatra, 74, who many here believe is seeking to manipulate her new populist, capitalist-friendly coalition government.

“I insist he is not trying to dominate,” the new prime minister told reporters after parliament elected her on Aug. 16 after yet another period of upheaval for Thailand’s stressed democracy. “I can think for myself.”

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But if it is proven in the nine-judge Constitutional Court that Mr. Thaksin is influencing, guiding or dominating his daughter or their Pheu Thai (For Thais) Party, he could be jailed, the party dissolved, and her government finished.

The young, untested prime minister, whose aunt, Yingluck Shinawatra, had her own star-crossed term as prime minister a decade ago, is finding her famous name to be a help and hindrance as she tries to govern in the wake of the stunning collapse of the previous coalition government of former Prime Minister Srettha Thavisin.

“Her weakness is being Thaksin’s daughter,” Rangsit University Political Science lecturer Wanwichit Boonprong said in an interview. Mr. Thaksin “has many political enemies,” Mr. Wanwichit said.

Ms. Paetongtarn has little political experience except witnessing the ugly, treacherous fate of her father and aunt.

After a 2006 military-backed coup, Mr. Thaksin plunged into self-exile for 17 years, dodging prison until last year when he voluntarily returned, spent several months in a Bangkok hospital, and was released.

The political dynasty suffered dynastic collapse again under Yingluck Shinawatra, whose three-year term in office was abruptly halted by a 2014 putsch, again with backing from the military. Today, the senior Ms. Yingluck remains a fugitive abroad avoiding a five-year prison sentence by the Supreme Court for financial mismanagement during her administration.

The next target?

After two decades of political backstabbing among the military and elected politicians, Ms. Paetongtarn, a mother of two, is being warned she is an easy target and may become the next Shinawatra to be prosecuted and pushed out.

The two coups against her father and aunt “weigh heavily on her shoulders, serving as both a reminder and a warning of the political perils ahead,” a Bangkok Post editorial said. “No one wishes to see her share the unfortunate fate that befell” her relatives, it said.

The new government in its first policy statements last month made clear reviving the sluggish Thai economy was a first priority. Heavily dependent on tourism, Thailand’s economy never fully recovered from the global COVID-19 shutdown. Growth in the first quarter of the year was a modest 1.7%, far below the pace of other countries in the region.

Thailand’s often murky legal system also presents pitfalls.

“Paetongtarn Shinawatra is also vulnerable as there is a pending case against her over the purchase of [Buddhist] monastic land by the Alpine Golf Club, a firm in which she is a shareholder,” said Chairith Yongpiam, a Bangkok Post assistant news editor.

Ms. Paetongtarn’s enemies are seeking any evidence to use against her and the Shinawatra-dominated Pheu Thai Party (PTP) for possible violations of the powerful Constitutional Court, which has a record of liquidating offending political parties and banishing even popular politicians.

The Thai Senate, packed by design with conservative supporters of the military, could be the source of that destabilizing possibility.

Senators launched the successful petition resulting in the Constitution Court ousting Mr. Srettha on August 14 for “unethical” political behavior because he appointed a lawyer who served time in prison in a bribery case to his Cabinet.

Mr. Srettha’s downfall enabled Ms. Paetongtarn to replace him, and continue as prime minister leading the PTP for its remaining three-year tenure, after a coalition reshuffle.

Balancing act

Ms. Paetongtarn is expected to follow her father’s past policies of maintaining close and balanced relations with both Washington and Beijing, allowing the U.S. to provide the bulk of the military assistance while China is encouraged to invest and develop infrastructure in Thailand.

But it will be balancing the domestic forces pressing down on her that may prove the biggest challenge. Conservatives linked to the military and the Thai monarchy retain significant power even though modernizing reformist parties scored big in last year’s national elections. The elections were held after a decade of power for a government effectively run by a military junta that took power in a coup.

“Whoever is in the Thai government must be able to work with the Thai armed forces, which still maintain close relationships with its U.S. counterpart,” said former Foreign Minister Kasit Piromya in an interview.

“Thailand has become less important in the eyes of the U.S. side, compared to Singapore, Vietnam, the Philippines, and even Indonesia. The new Thai government has to review and reposition itself first,” Mr. Kasit said.

During Mr. Thaksin’s 2001-2006 term as prime minister, President Bush welcomed him to the White House after Bangkok assisted Washington in the post-9/11 global war on terror groups. The U.S. and Thailand became non-NATO treaty allies.

Thailand’s close and comprehensive relations with China “were initiated by Mr. Thaksin himself some twenty-three years ago, and continued apace even when he and his nominees were out of power,” Bangkok-based Benjamin Zawacki, author of “Thailand: Shifting Ground Between the U.S. and a Rising China,” said in an interview.

Just how much influence the mercurial father will have on the untested daughter remains perhaps the biggest question mark.

“On the surface, Mr. Thaksin still dominates Thai politics nearly 20 years after he was deposed by a military coup and exiled for most of that period,” wrote columnist and Chulalongkorn University Political Science professor Thitinan Pongsudhirak.

“This time, his political power and influence are being exercised through his daughter Ms. Paetongtarn.”

“The irony for her now is that her father has struck an alliance with the pro-military and establishment forces who booted him out — as well as her aunt Yingluck Shinawatra — in the 2006 and 2014 military takeovers,”

Mr. Thitinan added.

Thaksin Shinawatra “reconsolidated his power in the blink of an eye,” the editor Mr. Chairith said. “Now we are again seeing old enemies bury the hatchet and vie for political cake.”

Coalition challenges

In addition to the family dynamics, Ms. Paetongtarn oversees a coalition government that consists of 10 political parties and one faction, holding 312 seats in Parliament’s 490-seat House of Representatives.

Wheeling and dealing in Thailand’s opaque politics will be a steep learning curve for Ms. Paetongtarn, whose master’s degree from England’s Surry University was in international hotel management.

Before bursting on the political scene last year, she was mostly unknown, growing up in her father’s shadow.

“I think she is trying to create an image of herself to be a representative of the new generation, modern, understanding technology and soft power policies in order to make Thailand as successful as South Korea [by] exporting cultural products,” said Mr. Wanwichit.

“Paetongtarn’s preferences mirror her father’s preferences,” Paul Chambers, a Thai political specialist at Naresuan University, said in an interview. “Thaksin appears everywhere that she goes. Thaksin is the major funder of the Pheu Thai Party. Only Thaksin loyalists have received top posts in Pheu Thai cabinets.”

Mr. Kasit, the former foreign minister who clashed while in office with the first Shinawatra government, noted that “nothing is known about her ideology or idealism or ideas. … She depends on her support team and her father.”