What a difficult and upsetting position you are in! Not only is this difficult for you, but for your children as well, no matter what age they are!
It is not impossible to salvage your marraige, but I doubt that it will happen on the timetable you would like. (sorry) Right now, it sounds like your husband wants distance. So let him have it. Are your physical needs being met, for you and your children? That is JOB #1. If your parents are prepared to support you over the long haul, then you can move on to the next steps.
Go ahead and consult a lawyer if you wish, but wait a couple of months before you DO anything. Use this time to get over the trauma of being abandoned, comfort yourself and your children, do some fun things with them. Reassure them that their dad still loves them and DON'T bad-mouth him to them. For one thing, he may come to his senses and be truly remorseful, and you did say you hope to salvage your marraige. Lots of couples separate for a time and come back together, stronger and better for it. My husband and I were apart for nearly 2 years, and now we've been back together for the best 14 years of a 28 year marriage! I cannot stress enough the importance of giving him the space he needs. For one thing, he may not even be sure of what he really wants right now, and he needs a bit of time to possibly discover what he threw away.
In the meantime, BUILD a new life for yourself and your children. Become independant. Become the person YOU want to be...make sure you take at least an hour or two for you at least every week to do something you love to do. I know exactly how hard it is to TAKE this time when you have little children, but you absolutely NEED it, and will be better for having done it. You need to start feeling good about You again, and rediscovering old interests is a great way to remind yourself that you are a worthwhile and interesting person. Sometimes in a marriage, kids, work and responsibilities take over and we can lose the person we are. You need to find that person again. (Sometimes, a spouse leaves because the person they fell in love with disappears in the sea of responsibility, and the joie de vivre goes away with it! This is usually the root of the so-called mid-life crisis, when people start to wonder if this is really all there is.)
Again, do not bad mouth him to the children. As time goes on, you may not even want him back. He may not want to come back. Trust me, as the children grow and mature, they will form their own opinions about you and their dad, based on your behavior. They will respect you for not having tried to turn them against him, and if he truly IS a schmuck, believe me, they will figure THAT out soon enough too!
This is a crummy situation to be in, and I'm sorry to say, it will probably take several months to sort a lot of things out. In time, as you work to re-build your life, and the lives of your children, you will re-gain your self-esteem (which always takes a battering when a spouse leaves). As you start to feel better about your life, and see what develops on his end, you will get a sure sense of whether your marriage is over or not. Then you can begin to act on legal advice and start proceedings for child support and alimony. Don't worry...the courts will go after him for back pay for the months that you got nothing from him if that is the way it ends up!
It can be trickier if he is in another country, but not impossible!
Try your best to address the issues you CAN, and wait a little for light on the ones you have no control over!
Most of all, don't despair! I know it seems very dark today, but the light is always at the end of the tunnel, no matter how long. Just keep on going. I promise, in the long haul, it will all be worth it. Even if you don't save your marraige, you will come out stronger, and you will be happy again.