If I am understanding correctly: you propose to have a 4x4 attached to the house - then ~2' of fence - a 4x4 gate post - and then the gate, hinge side to the 4x4 post. Given the 4x4 gate post is set in concrete and carrying the weight of the gate, I would not set the 4x4 attached to the house in concrete - not needed. I would ensure the 4x4 attachment to the house is very secure - preferably to studs, if possible, rather than just the sheathing.
I have a fairly heavy wooden gate, in a similar but different setting - it's hinge side is attached to the corner of the house, directly to the corner studs. One of the most solid 'gate posts' I have ever had.
I have a fairly heavy wooden gate, in a similar but different setting - it's hinge side is attached to the corner of the house, directly to the corner studs. One of the most solid 'gate posts' I have ever had.