If you do decided to leave the family home with the children, you will still be entitled to whatever your share/proportion of the property would be in terms of a later property settlement.
Some things to consider is whether or not you are in the financial position to move out, whether remaining under the same roof could lead to family violence, and, also whether refinancing the mortgage on your own, at a later stage, to possibly "buy out" the other sides share, would be a viable option (if offered) to enable you to remain in the family home with the children. If this would not be a option then it may be easier to move out sooner than later, if only as a means to "settle" the children into new accommodations. Property settlement orders, can at times, require 'quick' settlements, thus causing a need for parties to find new accommodations under pressure.
If you leave, while you should be able to make arrangements to collect your personal belongings, you will also likely need to purchase new items for the new accommodation. This can be expensive.
You should always seek legal advice prior to leaving the matrimonial home, especially if there are children involved.
The other parent is asking for you to leave with the children? Or are they just asking you to leave?