1. As per Section 7 of the Hindu Marriage Act, A Hindu marriage may be solemnized in accordance with the customary rites and ceremonies of either party thereto.
- Where such rites and ceremonies include the saptpadi ,i.e. the taking of seven steps by the bridegroom and the bride jointly before the sacred fire, the marriage becomes complete and binding when the seventh step is taken.
Hence, in the absence of 7 pheras , your remarriage was not solemnized according to customary rites and ceremonies , so,your said marriage was not a valid marriage.
2. A written undertaking can be challenged in future ,specially not getting the said custody from the Court.
3. As per law, no child or wife can claim any share in your ancestral or self acquired property during your life time
4. If she get registered marriage from the office of the marriage Registrar , then you can get the same from there, otherwise you cannot.
- Further if you get the proof of their marriage , then you can file a case under the Polygamy Act.