We have found Germany to be less expensive than most other countries. Often in Germany you can find B & B or small family run hotels that will charge for a room, then adding a third or fourth person is a fraction of the cost. Some charge per person and others just add maybe 20 euros for each additional person. If you plan to stay in one room, make sure you book ahead because there are not as many "family rooms" as double rooms. If you can find family rooms you would save money over getting two rooms. Often the family rooms will be more like a suite with two bedrooms.
In RS books, he usually will give a suggestion of what a trip will cost per person. We have always been able to be under his budget. We do rent a car, and I would imagine a car is cheaper than public transport for 4 people, but I'm not sure.
Look up and track airfare. Start checking it with some regularity so you will know if a good price comes along. I use kayak.com for international flights and I like googleflights.com too.
With research, you can easily come up with a good idea of what you will spend. Use Trip Advisor to scout out accommodations (go the actual hotel website), you can look up train travel (de.bahn), admissions to sites (on-line just look up). We usually eat a big breakfast (included in B & B cost) have a snack for lunch ( 5 E pp) and then go out to a nice moderate price dinner (20E pp or less) You can even look up restaurants on Trip Advisor for the area you are staying, check out their websites and menu and see what you might want and how much it costs.
I was really nervous about eating in London since I knew it was really expensive. I was able to scout out restaurants on Trip Advisor and found great places that we ended up going to. I had mock pre-chosen meals and knew what we would spend ahead of time. After looking up a few places I had a very good idea of what we would spend. I always plan high and we always come way under budget.
After a couple hours of research I think you will be able to get a fairly good idea. Plan a higher budget than you think and then it will be much more fun when you are not pinching pennies.
Have a great time! You will love Germany!