[SalesForce] lightning component ui:inputdate datepicker

Component's init handler is called long before scripts are loaded. So, You need to add afterScriptsLoaded={!c.methodName} to the <ltng:require /> tag, which inturn invokes the controller method where you can access the jQuery.

Here's an example:

component:

    <aura:component>
        <ltng:require scripts="/resource/jqueryDatePicker1/jqueryDatePicker1/jquery-1.12.4.js,/resource/jqueryDatePicker1/jqueryDatePicker1/jquery-ui.js"
                      afterScriptsLoaded="{!c.setScriptLoaded}"/>

    </aura:component>

controller:

({
    "setScriptLoaded" : function(cmp){
        console.log(jQuery);
    }
})

Right place to do DOM Manipulation is in the Renderer. You can use the afterRender to access the DOM.

Renderer:

afterRender: function(component, helper) {
    this.superAfterRender();
    console.debug('afterRender $: ',jQuery);
}

If using afterRender doesn't work, look at this answer this might help.

According to this Salesforce Lightning Roadmap, the ability to override standard actions with a Lightning Component is coming in Summer '17. (Take all forward-looking statements with a grain of salt.)

For the short term, I think you're stuck with the Lightning Out solution. You can't remove the New button from Recent Items unless you remove the ability to create new records period, which probably isn't what you want to do.