FHA requires you are 3-years out from a short sale, however less than 3 years can be acceptable if:
1. All installment (i.e. car loan, student loan, personal loan, etc.) payments & mortgage payments on the prior mortgage were made within the month due for the 12-month period preceding the short sale, and
2. You simply did not take advantage of declining market conditions, and
3. Are not purchasing a similar or superior property within a reasonable commuting distance at a reduced price as compared to current market value
It sounds like you would not fit the definition of #1. However FHA does go on to say that a lender can make an exception to the rule of being in default at the time of sale if
1. The default was due to circumstances beyond the borrower's control (i.e. such as death of primary wage earner, long-term uninsured illness, etc.) and
2. Your credit was satisfactory prior to the circumstances that caused the default
Job relocation isn't a circumstance beyond your control, depending on the amount of expenses and how greatly it affected your finances could be determined to be an extenuating circumstance. You'll need to be prepared with a letter of explanation with all of the details (including a timeline as that is certainly helpful to match up to the other events, i.e. short sale date, when you first went delinquent, etc.) and supporting documentation regarding your child's expenses.
If your child's expenses were not sudden and were easy to manage financially... and the *sole* reason that you went late on the mortgage is in an effort to get the lender to work with you, then that would not qualify for the 3-year exception in my opinion.
There are Fannie Mae & Freddie Mac financing options too, just requiring you to be 2 years out of a short sale (Freddie Mac goes to 90% financing 2 years out, Fannie Mae goes to 80% 2 years out - but PMI insurers are looking for 4-years out in order to go 90%), doesn't matter what the reason was for the short sale or if you went late or not.
FHA & conforming loan limits are decreasing end of September, estimated to be about $506k for King County, WA, but that doesn't look like it'll impact your loan amount.