UK Spoulsa Visa Gone to Appeal Process

Newbie here, would be great if the more experienced and knowledgable folk on here could guide me.

My wife is an US national and was living in the UK on a spousal visa, unfortunately in 2010 we did not extend her visa visa in time and applied 3 weeks after the time had elapsed.

We put an appeal in when her visa was refused as she applied within the UK (based on UKBA advice) - anyway fast forward 3 years the UKBA had still not dealt with the appeal and were still in hold of her passport (which they subsequently lost and not returned).

On their advice we decided to withdraw this appeal and return to US to make a brand new application - as it was extremely straight forward case. But this visa was refused on the income grounds, even though my salary (which goes into my wifes account)
is way above the income threshold they stated i had not met the income threshold eventhough all my wage slips showed a circa salary of £30k. As I changed jobs just before my application I was told I had not provided any income details for my new job. Now this was a much higher paid job but i was still negotiating my salary and had not received paperwork before putting my application in.

Another reason given for the refusal was that on my wage slips another name is mentioned than the company i put on the application form(common practice in business where trading names are involved). The rejection letter did specifically state that additional paperwork will be considered if the decision is appealed.

Question I have is that we have appealed and the date given is 4th June for the deadline for UKVI to respond to. Is it likely that the decision will be overturned or will they issue a court date?