You could try that route but the funds from parents would have to be declared as a gift, not a loan. You may not have to resort to that option, though. If you don't need to borrow close to the maximum amount that your combined incomes would allow, then some of the banks would be happy to approve an application where one applicant is still on probation. For example, if the affordability works on, say, your income and 50% of your wife's income, then I would be positive about the chance of getting approval. It would help if she is in the same type of job.
Even if you need her full income to be included to qualify for the required amount, any bank would issue an approval in principle with a condition that probation is completed before a loan offer is issued for a particular property. This can bring things forward by a month or two, compared to what you may have expected.
The property in negative equity doesn't help, but it may not damage your prospects too much if you have decent rental cover on it, i.e. excess of rent over the mortgage repayment (helpful if you have a tracker, of course).
Best regards,
Dave Curry (broker)
https://www.linkedin.com/in/davecurryirl