To establish a robust emergency fund, it's essential to calculate the optimal amount and create a sustainable plan for savings. Given your current financial situation, here are comprehensive recommendations tailored to your needs:

### **Optimal Emergency Fund Amount:**
Your monthly essential expenses total ₹50,000. Therefore, for a well-rounded emergency fund, you should aim for 3 to 6 months of these expenses:
- **Minimum:** ₹50,000 x 3 = **₹150,000**
- **Maximum:** ₹50,000 x 6 = **₹300,000**

Thus, your ideal emergency fund should be between **₹150,000 and ₹300,000**. 

### **Strategies for Building Your Emergency Fund:**

1. **Utilize Your Monthly Surplus:**  
   You currently have a monthly surplus of ₹50,000. Consider directing a portion of this surplus to your emergency fund. Setting aside ₹20,000 each month towards the fund will allow you to reach the minimum target of ₹150,000 in **7.5 months**.

2. **Automate Savings:**  
   Set up an automatic transfer from your salary account to a separate high-interest savings account dedicated to your emergency fund. This ensures you save consistently without requiring ongoing deliberation.

3. **Cut Non-Essential Expenses:**  
   Review your budget and identify non-essential expenses. Even a slight reduction can free up additional funds that could be channeled towards your emergency savings.

4. **Direct Additional Income:**  
   If you have any additional income sources, such as bonuses, gifts, or freelance work, consider channeling all or a portion of that into your emergency fund.

### **Maintaining Your Emergency Fund Over Time:**

1. **Regular Contributions:**  
   Continue saving towards your emergency fund even after reaching your target. Make it a habit to regularly assess your expenses and ensure that you maintain the fund at the minimum target level.

2. **Reassess Your Fund Needs:**  
   Annually review your expenses to adjust your emergency fund as your living costs change or if your family situation evolves (e.g., having another child).

3. **Avoid Unnecessary Withdrawals:**  
   Only dip into your emergency fund for unforeseen circumstances—job loss, medical emergencies, or major repairs. Replenish the fund as soon as possible after any withdrawal to ensure it remains a safety net.

4. **Invest Wisely:**  
   While your emergency fund should be liquid, you can park excess funds in interest-generating accounts. Speak to a financial advisor to explore options that suit your moderate risk preference without jeopardizing the liquidity you'll need for emergencies.

### **Integrating with Your Financial Goals:**

1. **Debt Repayment:**  
   With a total debt of ₹100,000, prioritize debt repayment while still saving for your emergency fund. This will free up more monthly income, allowing for higher savings rates in both areas.

2. **Setting Up SIPs for Goals:**  
   Create systematic investment plans for goals such as your house purchase and children's education once your emergency fund is stable. Investing while having a safety net reduces financial strain from sudden expenses.

3. **Insurance Coverage:**  
   As you build your fund, consider acquiring life and property insurance to protect your family's financial future in emergencies, ensuring that your emergency fund is for unexpected costs, not lost income due to inadequate coverage.

In conclusion, by establishing a clear emergency fund and integrating it within your broader financial strategy, you will enhance your financial stability and resilience against unforeseen challenges. Continue to assess your progress and adjust your plans as necessary, and you will be well on your way to achieving both immediate security and long-term financial goals.