Life is one long string of difficult and pretty major decisions!
When looking at retraining, I'd go for something you enjoy, are good at, and that's going to lead to a good job (hours/pay & conditions, future stability) - very difficult at the moment to see where the jobs market is going though! You need really good advice - from where, I'm afraid I don't know.
You need to keep your family finances manageable though, and going for a sizeable mortgage now is likely not a good option. The likely scenario is that the economy will trundle along at little to no growth, that the job market will contract and be a lot more competitive, and the really big one - that the property market is heading for a significant adjustment.
But regardless of what happens in the next few years, costs are increasing and becoming more of a burden right now.
FWIW, I think that buying another house now, at today's levels, and saddling yourselves with a large mortgage at unprecedented low rates of interest, would be a big mistake. There is a great deal of talk about affordability right now - trying to inject some optimism back into the market - but that is just looking at the monthly payments based on the lowest rates we have ever (and are likely to ever) seen. OK for a couple of years, but what then?
The likelihood is that you will find something to retrain in, get yourself a nice job when your youngest starts school and your family income will improve. At that time, the housing market is more likely than not to have either continued to flat-line (best case - but taking into account inflation, a subtle downward move) or adjusted significantly, so you will have more money, your deposit will be more and as a percentage, higher, and you will be in a much stronger position to buy again.
Meanwhile, negotiate a good long-term deal on your rented house (don't get me started on how crap the rental situation in this country is
- but hopefully doable if your LL is not just looking for a fast buck before selling) and save some dosh.
You are a trooper if you've read this far 