How much do you expect school fees to cost for the 13 year old to age 18? If they have been in private education all this time to be moved to state school at this stage will be difficult.
£3000 per month seems a big spend for one adult and two children. Could savings be made? Is a former lifestyle that can no longer be afforded being continued?
Hard for anyone to comment on your income as we don't know what living costs are where you live but what plans do you each have to maximise your income? You may not be able to increase hourly rate but you can increase hours worked to full time.