To begin, Filipino nationals require a visa to leave the airport. In your case you can get a Standard Visitor Visa or if your itinerary makes sense, a 48 hour transit visa.
Your itinerary is Germany - UK - Saudi Arabia, if the need for a transit visa is substantiated, i.e., it's the fastest or most convenient route, then you have a great premise. The constraint is that the maximum time you can spend in the UK is 48 hours. Note that they don't like it if, at prima facei, you have contrived an itinerary in order to create a premise.
If your itinerary appears to demonstrate an intentional visit to the UK, i.e., a destinational intent, they will refuse a transit visa application because you would need a Standard Visitor Visa instead. You did not provide enough background in your question for us to suggest the right alternative.
For your questions...
Are we able to go outside the airport during the layover in the UK?
Yes, provided you have a visa in all the passports. People spend time in the UK on transit visas to the extent that it's common.
What visa do we need to be able to tour a bit before our next flight?
The answer here is indeterminate because we do not have all of the information needed to suggest the best choice. You have two options: Standard Visitor Visa and Transit Visa.
To apply for either of these you can use the gateway at Visa4UK. Once you have entered your choice of visa, the software will guide you through the application process.
You and your family will also have to report to an Application Centre to enrol your biometrics.
Visa applications posted in the Schengen zone are processed through Croydon and take 5 - 7 days in most cases.
Your question also contains a question in its title...
How to enter the UK during a layover as a Filipino citizen?
Entering the UK is virtually automatic once the Immigration Officer has examined your visas. He will ask some questions and stamp your passports. Once that happens you proceed to the next room and you will have entered the UK. To flag a taxi or take the tube into central London, follow the "Way Out" signs into the main gallery and look for the appropriate signs.