Good advice has already given, just like to share my experience. Start as early as you can on the first day, like 4AM or near about is a good time because M9 (Khi-Hyd) is the best road in Sindh and you will reach Hyderabad at sunrise. From there onward you will have ample daylight and less traffic early on in the day.
Have breakfast at any dhaba hotel on N5 after crossing Hyderabad, and then take a rest at Royal Taj restaurant, Moro. They have got good washrooms and food. Assuming you leave at 4AM, you will have breakfast around 5:30-6:00AM and then easily reach Moro around 9:00-9:30AM. From there, you can target your lunch at Pano Aqil which is around 2:45 to 3:00 hours drive. So ideally, if all goes well, you will reach Pano Aqil around 12:30PM. There's a McDonalds right on the highway with clean washrooms, so you don't need to take a diversion.
From Pano Aqil onwards, you will find MdDonalds at Sadiqabad (about 2hours), and from there on, Bahawalpur is another 3hours drive. Why am I marketing McDonalds so much, you may ask? That's because you are travelling with family, and from experience I can tell you that my wife and children were the happiest whenever they saw a McD on highway. So in my opinion, you will reach Bahawalpur by 6:00PM at a steady pace with ample time for journey breaks in between. Take a good rest for next day's travel at any reasonably good hotel. Can't help you with that because I've no experience of the same as I broke my journey at Sadiqabad.
Start early next morning towards Lodhran, but just before reaching Lodhran, leave N5 and take E5, which will take you to Khanewal. Take the right turn to Khanewal bypass and rejoin N5 till Kacha Khu (about 2:30 to 2:45 hours from Bahawalpur). Leave N5, take the left turn towards Abdul Hakim and join M4 from there, as I've got no experience of that, I wouldn't comment further.
I hope that's helpful, have a safe and enjoyable journey. Regards
