It all depends on how much you want to take it.
There will be scenarios in any mental health job that direct you to get only what is needed. That's true for counselors, psychologists, psychiatrists, social workers etc.
Just one example: If you're working in a crisis psychiatry center, you will be directed to learn pretty much enough to direct the person for admission or discharge--if admission-involuntary or voluntary, if discharge--without or without meds, with a referral or not etc.
In such an environment--getting to really know your patient very well? IMHO no. You're just learning enough to follow the standard of care & process them. Of course over the years, you will see several (not all) patients on a repeated basis. You may also get to know them if you work in more than one aspect in the local area. E.g. if you work in the hospital, you'll see them in the ER, inpatient, and maybe even in outpatient if you do all 3. There are patients who become known like the back of the hand to several doctors in a hospital system.
However several psychiatrists only work in 1 job, and only interact with their patient in that context.
The bottom line is it really all depends on what you choose to do with it. I have seen doctors pretty much just throw a medication at a patient and limit their involvement to that. I do not agree with that approach, but hey, it happens, and to pretend it doesn't only adds to the problem. That is of course not the best of treatment. I've seen several doctors really get to know their patients well.
but I want to develop a relationship with my patients that goes on for years the same way that therapists do.
Such a thing is more likely to happen if you choose to work on an outpatient basis. In that setting you do see patients for years, and will get to talk to them about their long term issues.
(you won't be expert by the time you graduate),
Agree. I'm getting an impression that to truly be an expert in psychotherapy, it'll take several years of training, patience & dedication to that aspect alone.
Is psych residency a bit easier than the others? Is it possible to be a resident and have a family at the same time? thanks
This depends on the program. However in general psychiatry IMHO is much easier vs several other residency programs. This is in general. I have seen several psychiatry programs where one is worked hard in what most residents consider a malignant sense. However, don't kid yourself that residency is easy. While working 50-70 hrs a week without many all nighter calls is certainly easier vs other residency programs, that's still a lot of hard work, and you have to study for your exams in your free time.