I am so sorry to read that you have experienced such a loss and your feelings are very understandable given the circumstances.
It is both normal and necessary to go through a grieving process as a result of loss. Feelings need to be processed and it takes time to come to terms with a new way of life. Don't be surprised if your mood goes up and down, you may feel better one day and then not so good the next.
While you go through this do be patient and kind with yourself and allow yourself and your children whatever time and space you need.
Do ask for support from friends and family for yourself and your children, when you feel able, as it is a vulnerable time for you all and children can respond in unusual ways to grief that may seem unrelated (stomach aches, irritability, being distracted etc). There is also valuable support available through CRUSE (http://www.cruse.org.uk), an organisation who specialise in dealing with bereavement in both adults and children. Their website gives all sorts of information that you may find helpful, if you do not know about them already.
If you are an action oriented person it may help to gently create change around you as you adapt. This is a new phase in life and it can help to gradually change things in your living space. Tidy up, reorganise, clear clutter maybe even change the furniture around or paint a room a different colour. This change in our outer environment can help to change how we feel on the inside too.
When you feel up to it, try out new hobbies and see new places. Use this time to think about things both you and your children might like to try or places you might like to see that you haven't experienced before. Take a friend along and open your mind to new possibilities. When we undergo change that we would rather not experience our minds can get stuck in a rut. Doing something new can help the mind to see different possibilities.
Take exercise where you can preferably outdoors (weather permitting) as a way to lift mood and be sure to eat regular meals and natural foods. As far as possible avoid excessive amounts of sugar, alcohol and refined carbohydrates as these can cause blood sugar drops which will adversely affect your mood.
If you are NOT on any medication the herb St John's Wort has traditionally been used to help symptoms of low mood and mild anxiety. It can take a few weeks to work so you could also try a flower essence alongside which can help to rebalance emotions in challenging situations. There are a range available but Emergency Essence combined with Mood Essence would be one suggestion. If you are taking medication and/or would like further advice do consult with a healthcare practitioner or your GP or come back to me for an alternative suggestion. There is also a child essence which may help to support your children at this emotional time (provided they are over 2 years of age).
Thinking of you and sending very best wishes