The Turnbull government will get a step closer to delivering personal income tax cuts when parliament resumes on Monday.

However, while Labor supports the first part of the tax cut plan – lifting the 32.5 per cent bracket to $90,000 from July 1 – it won’t back the second and third steps until at least the government provides more information on their cost.

The draft laws are listed for debate on Tuesday and are expected to pass the lower house but the government may need to split the package to get it through the Senate in June.

The federal opposition is hopeful of getting the costing details from government officials during Senate estimates hearings, which start on Monday.

Labor will also seek updated figures on the cost of the coalition’s 10-year corporate tax plan, most of which it would dump if elected to government to pay for other priorities.

Weighing on the minds of Malcolm Turnbull and Bill Shorten – and feeding into vigorous debate in question time – will be five by-elections, two of which won’t be contested by the Liberals.

The date of the by-elections in the WA seats of Perth and Fremantle, Longman in Queensland, Braddon in Tasmania and Mayo in South Australia have yet to be set but are expected in July.

Senior bureaucrats and ministers will face a post-budget grilling during a fortnight of Senate estimates hearings.

Border Force boss Mike Outram will be grilled on the prospects of South African farmers getting refugee visas and a new health contractor for Manus Island.

Officials will also face questions over Home Affairs Minister Peter Dutton’s decision to allow two au pairs to stay in Australia despite arriving on tourist visas.

Environment bureaucrats will be asked about funding for the Great Barrier Reef, the national energy guarantee and the Snowy Hydro 2.0 project.

The government will also face scrutiny over changes to the work for the dole program in indigenous communities on Friday.

The government will introduce to the lower house tough new penalties, including jail time for dodgy live sheep exports, but the trade will be allowed to continue under new animal welfare conditions.

The sheep exports issue may also emerge in Senate estimates discussions with the Australian Maritime Safety Authority.

Legislation to implement the national redress scheme for victims of institutional sex abuse is on the cards, along with an amendment to crackdown on illegal tobacco importation.

The controversial drug testing for welfare bill is also listed for debate.