Rights of children of inter religion marriages

You are a Hindu. But you never got converted to Christianity. All your certificates show that you are a Hindu. Is it correct? In such a case there will not be any problem. By marrying a Hindu your wife will also become Hindu. Even though she has not changed her religion, as per Hindu religion, if a lady marries a Hindu boy, she will also be treated as Hindu only. So automatically your children will be Hindus only.
Your marriage is valid under the special marriage act provided you fulfilled all other criteria. So there should not be any problem if both of you are major's at the time of your marriage. So your children will have all the rights on your property.
If your property is ancestral property, your children will have all the rights on the ancestral property and if there is any problem in acquiring the same they can even fight the same in court. There are some cases in the court and they gave favourable judgements only for the children. If the property is your own earned, then it is your wish and you can distribute the same as you like. But you have to make a will to that effect. In the absence of any will made by you, your wife and your children will be the legal hires for your property and they will have all the rights.

According to your submission that you are a Hindu by birth but you you have married a catholic lady. If the marriage has been finalised with the mutual consent, the marriage is valid regardless the fact that both of you are not from the same religion. Even your marriage is valid under special marriage act and hence no problem is seen on that account.
Your children are your offsprings and they, too, will be treated as Hindus and they are entitled to enjoy all such ancestral properties which have been acquired by your father. If your father has any brother or sister, the same would be distributed proportionately.
In case of development of any problem in acquiring the property, this can be settled through the court though it may be a time consuming procedure sometimes. However, your children would get their due shares legally. If you make your will, the property would be distributed according to your will.

Thanks 4D clarification. Sreeram

Most of the Indian society are patriarchy society where caste, gotra and ancestral related everything run on the name of father. As told by you that you are a Hindu boy and married to a Catholic Lady. So, your marriage will come under special marriage act. Your wife and children would be treated as hindu religion. They are eligible to use all ancestral property as per provision. If any hurdle come on the way of acquiring property to your children then you can consult from lawyer. They will make you understand nicely regarding entitlement of your property.