If you're not finding sufficient time to practice the technique(s) then your instructor needs to make that time. If practicing each aspect of the whole method is difficult because of the other aspects then your instructor needs to isolate the interfering parts until your competence with each part is sufficient to leave more capacity to deal with more variables.
I prefer teaching wing down initially. There's more time & opportunity for the student to perceive what's happening, decide on a response & effect that response. It's also easier for the instructor to isolate parts for the student to practice.
Wing down: From a wings level crab into wind, yaw the aircraft until aligned with a reference point, usually the middle of the end of the runway. As the yaw is commenced use opposite aileron input (ie yaw left will require right roll input). Some of that aileron input will be to stop the secondary effect of yaw and some of it will be to lower the wing. You'll need an initially surprising amount input.
My thoughts about resolving your issue:
Have your instructor take you to somewhere with a long runway with a stiff, but not gusting, x-wind component. On the way there practice L & R sideslips up to full rudder deflection at lowish altitudes but stop/start the sideslip amount ie establish a small sideslip, then increase a bit, then a bit more etc. Do the reverse to reduce the sideslip.. The aim is to be able to hold the heading constant with reference to an external aim point while changing the AoB. The lowish altitudes are to help see the sideways component of the flight path.
At the long runway have your instructor demonstrate establishing the aircraft flying over the runway centreline in the wing down/sideslipping state. Lower the wing a bit more - while using even more rudder to keep the aircraft aligned - the s/he can move the aircraft upwind towards the runway edge. Maintain that position for a few moments then reduce the AoB/rudder input a bit to allow the aircraft to drift back to the CL. Stop the drift with more aileron. Start the drift again until over the downwind RWY edge. Stop it. Sideslip upwind back to the CL. Stop it.
While your instructor does this you need to have your hands & feet on the controls to feel how much input to make when it's your turn. Don't look in the cockpit, only at the external cues. Then it's your turn!
If co-ordinating all three axes + throttle is too much at first then your instructor needs to take over one or more of those inputs while you focus on a single one or two of them eg you control heading with rudder while your instructor does AoB, pitch & throttle. Once you're using your feet, then you can do the wing down while your instructor does the rest. Then you do both rudder & AoB, instructor on elevators & throttle (s/he should be able to move the column without interfering significantly with your inputs). Next you do rudder, AoB & altitude with instructor using throttle to hold speed. Eventually you'll do all of it under control while flying above the runway.
The next part is to reduce power gradually while still holding position over the CL. You'll need ever increasing control inputs as the speed reduces. When the wheels touch make sure the throttle is closed, continue adding more control inputs. By taxi speed you should have full aileron applied & whatever rudder is needed to counter weathercocking.
Your instructor should be **lightly** touching the pedals to feel what you're doing but *not* interfering with your inputs. You, on the other hand, should be pushing as hard as is necessary to make the heading go where you want.
Not everyone needs the method broken down into so many steps. You may not. Often the upper air practice is enough to bed-in the sideslip size of control inputs & co-ordination so the student can manage rather more when it's their turn to sideslip L & R across the runway.
One of the keys is that co-ordinating the sideslip control inputs needs to be as second nature as normal aileron/rudder co-ordination. Also a stiff, steady-as-possible wind so that your inputs are the variables, not the external environment. Lastly, part of an instructor's job is to off-load some of the workload until the remaining tasks are within the student's available capacity - splitting the job into manageable tasks which are then combined as capacity & skill develop.