Depending on the all the possibilities/circumstances what you have described can be complex and result in different answers.
It may be that your parents have a legal or equitable rights to a part of the value of your house or in the alternative, their contribution towards the house on your behalf can be considered in any property settlement.
In family law property settlement there are several factors that are considered to determine the division of property. Among the factors are;
1. Contributions to the welfare of the family, including home-maker contributions.
2. The future needs of each of the parties.
3. Financial contributions that are made directly or indirectly (e.g. by your parents) towards the acquisition, conservation or improvement of the property.
4. Non-financial contributions made directly or indirectly to acquisition, conservation or improvement of the property.
There are various other factors which need to be considered as well but at a basic level if one party’s contributions have been greater than the other then that will be considered and an adjustment can then be made in that party’s favour.
If one party’s future needs are greater than the other then those future needs will also be considered and an adjustment can be made in that party’s favour too. The circumstance of each party and person will be individually looked at and considered.
You have stated that you have children to look after which is an important factor, and you have also stated that your ex wife has gambling issues which can also be considered by the court. Gambling money during the relationship can be considered but it depends on the circumstances as to whether and how it affects any property settlement.
Ultimately, to get your wife’s name off the title of your property, your wife will need to agree to it, either that or you will need to negotiate a property settlement with her. That is the usual way it’s done.
Undoubtedly these circumstances are stressful, however, you both have rights which depend on all of the circumstances during your marriage and after separation.