Give yourself more time. Nine years is a long time and one month not very much to adjust to a completely new way of life.
Tackle the issues one at a time:
Feeling out of depth in your job: If your workplace hasn't offered appropriate on-the-job training, ask for it. Depending on the job, spend 30 minutes in the evening prioritising your tasks for the next day and working out what you need to be able to do them so that you are prepared and not flustered. Ask colleagues for help if you are stuck or ask your line manager to go through something again if you aren't sure how to do it. If your knowledge isn't up to scratch, timetable your day so that you spend a certain amount of time on research. If it's one where you are responding to emails as well as getting on with other tasks, timetable your day so that you spend a certain amount of time looking at and responding to emails, then a certain amount getting on with the task in hand e.g. get in, check emails and respond for 30 minutes, turn Outlook (or whatever) off for 45 minutes while you do X. Repeat.
Kids in the evenings: what is it that you can't cope with? How old are they? Having a faily council with your DH there could be hellpful in explaining to your children that things have changed and from now on they need to do xyz to get themselves prepared for the next day (laying out school uniform, sitting down to do homework from 5-5.30, having their bag packed). Again, timetabling is your friend. If everyone knows what they are expected to do and when they are to do it, there are fewer arguments and things take less time.
Childcare arrangements: are these stable? i.e. you haven't got the neighbour's cat looking after the children one afternoon, then your bezzie mate doing it the next day etc. If not, look into a childminder who does drop-offs and pickups at your children's school, the school breakfast and after-school club and reciprocal arrangements with other parents who need childcare when you work short days.
DH not home: Work out with him the day or days when he will certainly be home by x o'clock to hear Timmy read, bathe Emily and put both to bed. Make sure it is an arrangement he can stick to so that you are never unsure of what you have to do each evening.
It might look from the above that you are starting a military academy but feeling more organised and certain of what you are doing can help all of you feel more in control. Make sure you have some time for yourself so that you can unwind or go out with friends too. No one expects a new employee to be perfect at what they do in a month and no one minds repeating or demonstrating something so that you can get it right.
Good luck!