My advice put the house on the market ASAP if you want to move. A house sale will take approx 12 weeks to go through. Get mortgage approval at the same time it doesn't take long.
No seller will entertain you if you still have your own house to sell. No buyer will entertain you if you are only going to move out if/when you find somewhere to move to.
You have to be prepared to move out and rent if that's what's required.
Sell first, rent, buy again. I know the renting is another painful step, but trying to sell and buy yourselves again at the same time is a lot more pressure than selling, renting and then buying.