I think I grasped your question correctly: you want to redesign a web site, and the accompanying native app should look similar to it. You need a native app for certain features like push notifications.
By going down the native route it would require you to override the GUI controls in whatever platform and redraw these controls to look how you designed them. This can be as simple as
this.button.ForeColor = Color.Red; but you would only be changing colours and not have very much control beyond the colours and font.
Redrawing is actually fairly complicated, and StackOverflow would be the better place to ask for help with that.
There is also the option of creating a web app in a native wrapper. I believe Phonegap et al can achieve this although I have no experience with them myself. As we saw with Facebook's u-turn on a HTML5-based mobile app in 2012 though - users wanted the speed and responsiveness of native.
It's worth considering also whether your users will be expecting the SAME UI on their phone as in their browser, or just one that shares the same theme. Compare the reviews for an app that is released with Google's Material design with a previous version without it. There is usually a huge difference and the users are preferring a material based app using native UI controls rather than a custom UI controls, even if they are native.