Do you intend to use the money you get from your house to pay towards the rent for a nicer house? Think very carefully. At present things are hard for you financially but in ten years time you will have finished paying your mortgage and will probably be better off when the children are off your hands. If you are paying out for rent you will be surprised how quickly it will fritter your money away. You might feel richer for a bit, but the worries will come later on. There will also be the temptation to spend more money initially once you have the proceeds of the house.
You can make a really nice home from an old terraced house. A really gorgeous house might seem tempting, but I would stick where you are and make your house as nice as you possibly can. It might be a bit crammed but your children won't be there forever. Besides, a gorgeous house doesn't necessary mean a nice home. Home is where your family is and where you feel safe and secure, no matter how lowly your home may be.
Think very carefully. However, it ultimately must be a joint decision and you must be certain that what you do is what you really want. There can be no going back.