Here in Germany, being a single parent is one of the “best” indicators of poverty: Your income would most likely shrink due to reduced working hours needed for taking care of your son. Which, in return, makes it more difficult to pay off loans long term. It also highly depends on the flexibility your employer is willing to offer you.
Given your short description of your situation, my spontaneous advice is:
- Stay with your parents and continue splitting responsibilities. As long as everyone is OK with the situation, there are many upsides to this: You can earn good money, while your parents get to see their grandchild on a daily basis, etc.
- Buy the house and rent it out. At the moment it might be best to stay with your parents, but this might change. In the best case, you meet a new partner with whom you want to live and share responsibilities together. In the worst case, there might be a falling out between you and your parents, and you have to leave their house. Renting out the house before you need it will help you pay off the loan faster. A word of advice, though: Being a landlord can be a double-edged sword. The current tenant of my grandmas’ flat basically just sleeps there during the week and drives to their partner for the weekend. But she also had a tenant before who stopped paying rent for months and then vanished.
Can only speak for Germany, but here the term to look out for is “Eigenbedarfskündigung”.