i would expect my partner to discipline my kids the same way i would or even better. The disconnect with the step parents happens when the child is handled like a hot boiled egg every-time disciple is required. If your parent (step or not) disciplines you its a sign they care and are invested in your well being.
The moment you decide to have a new future with someone and they are children are involved, its fundamental that both of u let the children know from the getgo that u're unified and one on every decision. Never raise children with different discretionary disciple measures esp if both of you are coming in with your own kids
We were whiped as kids and it got us in line...

but its different with these generations that came after us

good luck.