Broadly agree with much of the comments above by Brendan. Though I think you need to be very cautious here and not 'dig a hole'. Appreciate that is the basis of your queries so you are clearly doing the right thing in seeking advice.
Agree completely, it does not make financial sense to rent a house. It does not improve your situation and if anything I believe that it will become more, not less, difficult to buy in 5-10 years based on your facts.
Is it practical/does it make sense to buy another intermediate house? I understand the logic, pros and cons. Reality is a lot of people did this, the so called 'starter home/apartment' and it didn't work out. I would advise against another intermediate house based on the facts here. Much of your current funds will be depleted in 5-10 years, and it could well be near impossible to move again. Also you don't indicate your ages, guessing you are mid 30s (as you bought apt in 2006). A key advantage you have now is a healthy deposit so I would use it wisely, well done on saving by the way!
Re your salaries, take home pay, etc, and given you have a child, I think you are being overly optimistic regarding what rent and savings you could make per month. Rent 1,900/2,000 plus savings 800 per month?? That equals 33k/34k per year. Given current salaries your net combined take home pay is somewhere around 76k/77k per year. You are suggesting setting aside 43-45% of your net pay for house purposes (33k/76k). Have you considered childcare, other costs, etc? Additional children perhaps? How secure are the jobs, salaries?? May well be that with tightening the purse strings you could do it for a year or two but at some point the pressure would come on.
Re the apt, don't forget that the fixed rate of 3.8% may be below the banks standard variable rate, if the latter was, say, 4.5% your monthly repayments would increase by around 200 per month once you're out of the fixed period to allow you pay your existing apt mortgage within the time period of 22 years.
From a financial viewpoint (indicative figures only provided as an example):
1 - Say the Bank did allow a negative equity mortgage and using Brendan's figure of 526k, ie also sell the apt. Over 25 years at 4.5% it would cost about 2,925 per month. This would take almost half of your combined take home pay to fund. Add in other costs with owning a house (insurance, taxes, repairs, etc) seems to me that this is a stretch too far, particularly over the longer term. (Extending the mortgage to 30 years would still cost 2,700 per month, so I don't think I would do that). Bank are unlikely to do this anyway.
2 - Same facts as 1 above, except you buy a house costing 400k not 500k, so borrow 426k. Monthly cost 2,370 @4.5% over 25 years (lowers the monthly cost by around 550). This reduces the % of your incomes to around 37% of your take home income for the house, this is more in line with suggested/recommended levels and is probably a more sustainable figure. Could you lower your expectations on the house you needed a little? This would still take persuasion of the Bank though it could be more achievable. You seem to have a strong track record.
3 - Lets say you kept the apt and rented it. I assumed 1,000 per month in rent (purely for illustration purposes). Keeping the existing mortgages, allowing for taxes, repairs, etc, I calculate you would need to fund the apt mortgage to the tune of 10-12k per year. The majority of this is the additional mortgage payments over and above the rent, also allows one months vacancy per year, modest repairs and bills. Based on the numbers, keeping the apt is certainly not an option if you want to buy from an affordability viewpoint. Also seems that you have little chance of saving 800 per month if you rent at 1,900/2,0 per month and also need to fund the rented apt by 800-1,000 per month. Any money saved would simply go to the apt mortgage/costs (These are fairly realistic figures by the way, could dispute 100-200 max perhaps, but it wouldn't change the overall position or views significantly).
Having looked at the numbers number 2 seems to me financially the most practical way to achieve your overall objective of owning a house. Can you get a house at max 400k and it meet your needs?