I cannot comment directly on your case without specifics such as ages, incomes or assets. However, I can provide some general principles:
1) Normally when someone moves out of the family home and pending the final order on finances, it is normal for the occupant spouse to pay the mortgage in full and for the non-occupant to pay only
child maintenance. If the non-occupant is a particularly high earner it may be possible to get maintenance pending suit that can contribute to the mortgage but a solicitor would advise him not to pay anything above CMS maintenance unless ordered to do so as this would demonstrate that he could afford spousal maintenance in the long term.
2) You say you work part time and term time only. However, the court normally uses universal credit guidelines as the amount of time that you should be working. If any of your children are under 3 your current role may be acceptable to a court. Between the age of 3 and 12 you will be expected to work an average of 30 hours per week throughout the year. Once the children are 12, you will be expected to be working full time. If you are not currently doing these hours the court may give you a year or two to adjust but after that they will impute a full time income to you as the earning capacity upon which any settlement is based.
3) This will similarly affect your ability to get a Mesher Order. Mesher Orders are extremely rare in a contested outcome. Mesher Orders until the children are 18 are rarer still unless the youngest child is already within a few years of reaching this age. Solicitors will still suggest them as they are not uncommon in
Consent Orders but most people are unlikely to get one unless their ex agrees to it. What is more plausible is that one person can stay in the house until the fixed term on the mortgage has ended and then the house is sold.
4) One thing you need to bear in mind is that the courts will be acutely aware that your ex will be stuck on your mortgage whilst a Mesher Order is in place. Whilst they cannot order a bank to remove him from the mortgage, another approach with the house is that they transfer it to you (he would either get a deferred charge on it or
offset it against any pension) and then you will be given a set date in the future by which time you must secure his removal from the mortgage. Failure to remove him from the mortgage would then trigger a sale. Depending on the ages of the children, a settlement like this might give you up to 5 years before you have to sell.
5) To consolidate and explain the above, the courts will be very keen to get a
Clean Break between you at the earliest opportunity. Gone are the days when the lower earner can claim that because of a "marital decision" that they stay at home, they should be dependent on their ex for ever or even until all the children are 18. The courts are rightly sceptical about such claims for compensation nowadays, especially when the lower earner did not have a career before children. It is almost always the case in contest divorces nowadays that there is a clean break within 5 years.
