It really depends upon the circumstances.
There is a legal argument that if one party enjoys to sole use of a property and they can afford the mortgage they should pay the whole mortgage, their share and the other party's in lieu of rent for occupying their half of the property. After all the other party has their own living costs to pay.
However, there is an obligation for spouses to maintain each other and if the party left in the property is struggling and the party who left the former matrimonial party can afford to contribute they might find themselves going through the hassle and expense of court proceedings for maintenance pending the final financial settlement.
Either way if your husband is the primary carer he should be in receipt of Child Benefit, Working Families Tax Credit and child support from you.
The actual divorce and finances are treated separately and you need to ensure there is a court order settling the finances so neither party can make future claims against the other. To make an order which is agreed difficult to challenge it needs to be fair (within the s25 Matrimonial Causes Act 1973 criteria there should be full disclosure, legal advice. There is little point in economising with this.
It is possible to defer the sale of the house by the way of a Mesher order. Your interest in the property would then be held until a condition triggers a sale. The usual conditions are the remarriage or death of the PWC or the youngest child reaching 18 or finishing tertiary education. Alternatively your interest can be maintained as a chargeback which has to be paid to you on a certain date.
There are capital gains tax implications because you only have CGT relief on your main residence and as you know longer live there CGT may kick in after three years. Therfore it's a good idea to speak to a lawyer in good time to find out exactly where you stand in your particular circumstances.
BTW there is no such thing as a quickie divorce in England & Wales. Whether you use a solicitor, online company or do it yourself the procedure is exactly the same. There is no reason why you can't download the petition, Form D8, guides D183, D184, D185 and EX150 (court fees list) from HM Court Services website and complete the form yourself. You then send the form, fees and your marriage certificate to the court.