I agree with your health visitor, baby needs to learn to go to sleep in the cot and that all settling will be done in the cot.
It is probably the very reason and cause for her waking so frequently. Humans have small periods of semi-consciousness all night long. They don't ususlly wake up properly in these periods, in an adult it might involve changing positions, pulling the duvet over yourself, unconsciously glancing at the clock and back to sleep.
These are often calked 'environment checks' - like that the caveman needed to ensure he was safe and protected from predictors whilst also sleeping.
Imagine you went to sleep in your bed and then an hour later when to roll over and stick your leg out from the duvet and you suddenly realise you are in the back seat of a car. You would not just roll over and go back to sleep. You would be wide awake and wondering wtf happened within seconds. This is what is happenibg with your DD when she goes to sleep in your arms, secure at your chest, hearing your heartbeat and smelling your smell. Then rolls around an hour or so later and finds herself in her cot and on her own.
If she's going to go to sleep physically close to you, in your arms like that. Then in order to sleep well, she needs similar conditions maintaining through her environment checks. This will involve bed sharing and co sleeping.
If you are expecting her to sleep in her cot, this is where she needs to go to sleep. From fully awake to fully asleeasleep all done in the cot. Same at bedtime and all night wakes.
Try the 'firm hand' technique. Firm hand on baby's chest or back. I'd add in a dummy to suck to reduce crying but that's up to you. Don't push down with your hand but the idea is baby can feel your hand there even with eyes closed and relaxing.
Other hand might be holding kicking legs still, or stroking hair or patting or whatever you feel works best. Aim for still, quiet and calm where p osdible though. And stay there right through until fully asleep.
Don't be tempted to pull away once calming down, keep that firm hand on chest/back and stay right there until fully asleep. Then leave ninja style once asleep.
Repeat every wake up. Every bedtime and naptime. Utter consistancy.
It won't be easy and it won't be a magic answer to give you an independant sleeper from Day 1. But it is the first step towards this.