The new UUP leader has dismissed calls for a single unionist party.
Robin Swann said such a move risked driving unionists into the Alliance Party or leaving them with nobody to vote for.
He also promised his Stormont team would not join the Executive if political agreements were made solely for the DUP and Sinn Fein's benefit.
And he called for a funding boost to remove people from health service waiting lists as it struggles without a health minister to make decisions.
Mr Swann said: "We have a daughter of six and a son of four - I want their experience of growing up in Northern Ireland to be very different from mine.
"I want them to grow up in a Northern Ireland at peace with itself, a Northern Ireland for all its people, a Northern Ireland which has a particular emphasis on the development of our children, which respects its elders and looks after the vulnerable."
He was confirmed by a party meeting in Belfast as the replacement for Mike Nesbitt, who stepped aside after the UUP's disappointing showing in the March 2 Assembly election.
A Sinn Fein surge at the polls to within one seat of the DUP has led some influential voices to call for a single unionist grouping.
The new UUP leader urged them to consider the consequences of such an outcome.
"A single unionist party would limit choice, stifle debate and quickly result in the depletion of unionist votes at the ballot box.
"I am in the Ulster Unionist Party - we are in the Ulster Unionist Party - because we believe in its vision, its policies and its priorities.
"No other party comes close to representing the brand of unionism that we have and I believe in."
He added: "It would also run the risk of driving those who consider themselves unionists, but only with a small U, into the arms of a party which is at best agnostic to the union, and it would leave many others with no-one to vote for at all."
The UUP returned 10 Assembly members, down from 16 before the recent election during which the number of seats available was reduced.
The five main parties have until next Friday - Good Friday - to form a new Executive or direct rule could be reintroduced.
The North Antrim Assembly member added: "And whilst I do not rule out any possibilities, if these talks end up being talks and agreements made by two parties for the benefit of two parties, then I say let it be an Executive of two parties.
"Standing at the great height of 5ft 3ish, I have had my experiences of people trying to bully me and push me around... trust me - I have never been pushed around, nor do I intend starting to let people push me around, nor will I allow this party to be pushed around.
"This party did not take the leap it did almost 20 years ago to see parties continue in a cycle of never-ending negotiations."