I want to commend you and your husband for at least knowing that you want to continue co-raising your children, and being aware of their needs. Staying married for the kids is not always the best option, but you did not write to me for advice on that.
So, as for the sexual component of your life, there are a few things you can do. You have stated that you have tried putting the spark back into the relationship. I do want to challenge you to truly examine your efforts. Sometimes, when we are truly fed up with a situation, even the most minute effort seems strenuous. I ask that you really analyze what you have done, and if it is ultimately enough for you to feel that you are looking at other options honestly. (Read more in When Sex Dries Up: How to Get Your Sexy Back.)
At the same time, you say that too much has happened for you to mend your sexual relationship. While there are no details, I can empathize that sometimes we do hit a point in which we can no longer attempt any new (or old) method to rejuvenate desire for someone that we hold a lot of negative emotions for. That part of the relationship is gone, and you are left to move forward.
Please note, the suggestion I list below is without knowing anything about your context. The most obvious choice for you is to reconsider divorce, but if you and your husband are adamant about maintaining a nuclear family setting while your children are young, an open marriage may be another option worth considering. Have you and your husband discussed possibly staying married to co-raise your children while each seeking sexual/intimate fulfillment from an outside party? An open relationship may be the compromise you both need in order to sustain your marriage.
You say you are too young to be sexless but cannot bring yourself to engage in sexual activity with your husband. Do you find other men attractive? Do you still wish to have a sexual relationship? If the answer is yes, then perhaps you should consider this. Before bringing up the idea, however, you must be very clear when communicating. Sex with someone other than the man you married is still going to damage his ego, not to mention hurt his feelings. Also, before pursuing this line of thought, you will need to consider if you can handle your husband being sexual with another woman. This has to begin as a two-way street, even if both parties do not opt to participate. Honesty is going to be your very best option, not just with your husband, but also with other partners you may choose to have sex with. Honesty with yourself is of utmost importance. Rules would need to be established, along with very clear boundaries for all parties involved. While working through all of the nuances in your head, remember to ask yourself if these are conditions you can live with. Do not expect this to be solved overnight.
I cannot promise that this is your answer; your husband may very well hate the idea, and lobby for divorce over an open marriage. Exploration of this as a possibility will at least open your mind to other possibilities. I hope one of them will work for you and your husband.
