Right, all of this thread seems to be focused on solving the problem of how to keep the OP's mother caring for her children outside of school hours. There are other ways though.
Firstly, I'm all for sending children to their local school for the reasons a lot of people have stated above - playdates, parties, etc. It doesn't take long for kids to start wanting to do after school activities - football, cricket, music clubs etc, and they can help keep a child an hour longer at school if that helps your pick up times. Also most schools will have a before/after school club that shouldn't cost much and can be paid for out of childcare vouchers - if you don't use your tax-free childcare scheme, now is the time to get on it. Effectively the end result is that you pay for childcare out of your pre-tax income, offsetting tax. Our school's before school club is £3.50 a day, so £17.50 a week which after tax offset works out at about £13.50. I reckon your travel costs 15 miles each way, each day would come in at lots more than that.
Once at school if you get to know other parents (much easier if they are very local to you too) you'll realise that there are other parents in the same situation as you, who may help you with lifts in exchange for you helping them. Eg I work nights at the airport, another mother of a child in my son's class works nights on a news desk. We frequently help each other with lifts to and from school.
Another idea is have you tried asking your employer for flexible working? You are entitled to ask for it for childcare purposes. They are not obliged to grant it but they must seriously consider it. One woman that I work with took our employer to court twice (first time our employer argued with the courts and tried to appeal, but she won each time and it is thanks to her leading the way that I now work 50% because of childcare.) You can ask for your hours to be compressed, for permission to work from home or for your normal hours to be slid to accommodate your school drop off/pick up times without it affecting your income. if you haven't talked to your boss about this, then go to see them armed with the facts and speak to someone in your HR department (if your employer has a HR department.
Finally, no one has mentioned the elephant in the room here - what contribution is you DC's father making to their care? He should not be leaving you struggling to afford childcare even if you are no longer together. He is still their father and should be financially supporting them.
There will be poster here more knowledgable than me about issues such as claiming support from your ex-H and claiming benefits for assisting with child care if you are on a low income. But these avenues, along with flexible working and building a local support network of other parents are much more feasible in my mind than relying on your mother who is by default an older person and who lives miles away for the foreseeable future.