Of course - your spouse should definitely continue trying to negotiate with the other parent for more time with the child. To give you an idea of why I always say this, refer to a case published today by the Federal Circuit Court.
In this particular case, one parent moved unilaterally on two occasions and refused to facilitate time between parent and child. This is what the judge had to say about a series of text messages in which the parent does not respond, nor make any other effort to ensure the child can see the other party:
It is troubling when one looks at these messages. It is quite clear that the father was seeking an ongoing relationship with the son and that the mother was aware of this although she denied receiving all of these messages initially, but this was clarified when she produced her telephone on Day 3. The mother ignored his requests from 16 January 2014 and subsequently relocated to a place unknown to the father.
Further, when asked about the relocation and if the parent regretted it, the judge noted:
She never said that she regrets that the father and the child did not have an ongoing relationship. She never said she regrets her son not having seen his father for that period. Her regret, in my view, was too little too late and not focussed on the real issues that surrounds the best interests of the child.
Granted, you can't make assumptions about the outcome of a case based on any single, or even cumulative, judgment handed down by the court, but it is consistent that court doesn't take to parents who don't recognise and facilitate a child's relationship with the other parent. Similarly, the court always takes well to parents who continue trying.
I'm sorry to hear your partner will be out of the job at the end of the month, but don't stress too much on that in terms of the parenting issue. The court will be unlikely to give it significant weight because at the end of the day, parents can't predict when they're going to be made redundant, and employment doesn't determine a person's parenting capacity or relationship between parent and child. Provided unemployment isn't going to make you homeless, it should not be an issue.
Finally, I would still advise at least applying for Legal Aid. It takes into account a large range of considerations, including likelihood of success, not just household income. If you don't get it, fine, but you should at least try.