Try putting the pressure tester on either another hose bib (if you have another) or connect it to your washer hookups. The front hose bib is before your problem area, so the pressure is not changing. Checking the pressure at the washer will help you figure out what the pressure inside of the house is.
Flow (GPM) depends on pressure difference and resistance. If your flow is dropping, either the pressure at the street has changed (and you have verified that it has not) or something in the house is causing a very high pressure drop. With nothing flowing, everything in the house should be at street pressure (60 psi). There can be a variation it this pressure +/- a few psi due to elevation change (2nd floor vs. basement), but it should be pretty close to the street pressure. Even if your pipes were nearly completely blocked, you should still see 60 psi everywhere when everything is off. If that checks out, turn on a sink to the tub and look at the pressure again (at the washer). If everything is normal, the pressure should only drop a bit when something else is flowing.
If the pressure drops a bunch when you turn something on, something is causing a large resistance. Start by checking mechanical things (verify valves fully open, PRV is good (if you had one), check the softener, etc.). What type of pipes do you have and how old is the house? Galvanized pipes can close up on you over the years, but it is normally a slow progression.
Another thing you could do is to measure GPM. Take a 5 gallon (or whatever) size bucket and see how long it takes to fill. Try to start where the water enters the house (hose bib) and then check tub, washer, sinks, etc. Some things will natually flow more water than others (tub spout vs. bath lav), but if you record what you are getting and report back, we can help to tell you if it is "normal" or not. Have someone look at the pressure tester when you do this and see when you see a big pressure drop.