Essentially the starting point with dividing what is normally the main marital asset - the family home - is that proceeds should be shared on a 50/50 basis.
Anything that mirrors this is a fairly safe bet.
However, as you are the main carer for your children, you may be allocated with a larger than 50% share in a final hearing, so by selling up and sharing the proceeds now you may be worse off than if you wait. However, you won't normally get a final resolution at the first court hearing, so your final hearing may be some 6-12 months later than the October date. So it is a case of weighing up the options now, and also if the equity in the property is relatively modest obviously the impact is less than if there is a significant amount of equity to consider.
You will struggle to bring the court case (initial hearing date) forward.
You could consider filing an application for interim maintenance in the meantime.
Interim maintenance is usually spousal maintenance, but there could be an interim CM application as far as I am aware.
Have you both filed form E's?