do it your own rather than agency

I am a UK nurse with 8 years experience and want to go to US to work. I have passed the nclex and Im taking ielts this month. I'd like to work this myself rather than having an agency in which you're tide up(That's what I thought). I have a good job and some properties in UK and I'm not on a hurry to go to US specially now with some issues about retrogression. Weather, hoping for a better pay,better house, and better education for my children are major reasons for the move. My questions are:

1. IS doing it myself better than having an agency to work on this move?

2. I've seen some adverts that says 35 days paid leave. Is this true is USA?

3. Would I be paid better if I apply direct to the hospital than on agency?

4. Does agency have better access or prioritized more than individuals who applied on there own?

5. Apart from how much you earn, Is this idea of moving to US would give me better time and life for my family?

I think you all get my whole point here. Please if anyone could give me advantages and disadvantages of doing it on my own than agency. Is it worth to move?