Child dying, wife deserted, conversion and marriage

Without divorce you can not re-marry. As far as child health isconcerned, take relatives, friends help. After all it is the question of child life. Any body can help for life protection of a child.

There is no point in converting to Islam for the sake of remarriage bcoz the subsequent marriage done without first obtaining divorce from your present wife shall still be void and also you will expose yourself for any action of bigamy and series of some other criminal cases from your present wife which will only increase your troubles. So, it is better if you first obtain divorce from your wife and then remarry.

But She is not Ready to give the divorce even ? I am scared that a contested divorce will take a long time. How much time is expected in contested cases ?

True that contested divorce takes more time, but the matter will be resolved once forever. If you marry illegally, your wife who is not ready to give you divorce, can make your life a hell by making you run around courts by filing various criminal cases against you. See if your wife can be given some understanding through some friends or relatives. Your in-laws also must be understanding your situation bcoz of the ill child. Try to resolve the situation amicably if possible.