Replace fragment with another fragment inside ViewPager

I'm using a ViewPager together with a FragmentPagerAdapter to host three different fragments

[Fragment1][Fragment2][Fragment3]

What I'm trying to achieve is to successfully replace Fragment1 with a whole new fragment, Fragment4, if a specific task succeeds.

When I use..

FragmentManager fragmentManager = getSupportFragmentManager();
FragmentTransaction transaction = fragmentManager.beginTransaction();
transaction.replace(R.id.fragment1_layout_id, fragment4);
transaction.commit();

..the fragment is replaced beautifully and Fragment4 is shown instead of Fragment1. Though as soon as I swipe all the way to Fragment3 and then back to Fragment4, Fragment1 has made a comeback.

Then again, if I use..

FragmentManager fragmentManager = getSupportFragmentManager();
FragmentTransaction transaction = fragmentManager.beginTransaction();
transaction.remove(fragment1);
transaction.commit();

..Fragment1 is removed and when I come back Fragment4 is there. So the problem with this solution is that I couldn't find a way to immediately show Fragment4 as Fragment1 is removed, even if I tried:

transaction.add(fragment4);
transaction.show(fragment4);

And here's how my FragmentPagerAdapter implementation looks like at the moment, without any transaction managing:

public static class PagerAdapter extends FragmentPagerAdapter {

    public PagerAdapter(FragmentManager fm) {
        super(fm);
    }

    @Override
    public int getCount() {
        return VIEW_COUNT;
    }

    @Override
    public Fragment getItem(int position) {

        Fragment fragment = null;

        switch (position) {
        case 0:
            fragment = Fragment1.newInstance(context_);
            break;

        case 1:
            fragment = Fragment2.newInstance(context_);
            break;

        case 2:
            fragmen