Renting in another state

Hi sorry for the long post. My husband and I need some advice. We currently live in a major city and can't afford to live here anymore. Husband changed occupations last year to get a better paying job, keeps doing courses and training etc to try and better our life, but it just never seems enough, the more he earns the more rent goes up. As a teen mum with no support 8years ago, we were almost homeless and moved into government housing, which was a God send. I did some study and work etc but child care here is just to expensive and we became financially worse off with me working, as half my pay was going to child care even with the rebate and rent went up because I was working to, paid parking was min$30 a day and I needed to drive, etc. We have 3 children living in a 2 bedroom place. We originally thought we could just move to a private rental but the cheapest place we have seen, even 30-45 mins away was $530 for a 3 bedroom 1 bath. We would both need to be working full-time without the cost of child care to come close to affording it and without support its not doable here. We need and want to move. I want to give my children so much more from life and at the moment we can't. I feel like I'm failing, there is only so often a picnic at the park is exciting but we can't afford to do much else. Our issue is how do we move? So many places are more affordable to live but being mid 20s with no rental history and no support at all (my dad is an alcoholic, mum is a narcissist, hubby's mum is in full-time care due to a brain aneurysm) how do we make this happen? All job positions hubby has looked at in different states are casual with ongoing work for the right person or full-time for people with 3+ years experience. As he is good at his job we're not worried about him not having employment, but that doesn't look good on applications. How can we get a rental application look good while in a different state? How do you apply for rentals and jobs without being there? We are becoming so unhappy here and it's beginning to take a toll on everyone's relationships in the home, without having at least a game plan on what to do next. We are able to use my neighbours as references as we get along well and they own there place, we do take pride in our home but don't have anyone else for any more support. Any tips and advice is greatly appreciated. Thank you