Can a occupancy sensor switch and a timer switch be installed in the same three way circuit?
Keep in mind, you're asking quite a lot  here.  You want a 3-way switch (why?), and a motion sensor, and also a time of day timer only because your sensor is not performing to your satisfaction.   Also you are driving 8 flood lights which I suspect exceeds this sensor's rating.  And you bought a "no neutral" switch which makes me think you don't have a neutral. 

Let me be blunt: it isn't gonna happen like that.  It can't.  

3-way switch

First, think through this "3-way" business. How is that supposed to work? If you throw that switch, will the light come on for 5 minutes? All night? Forever?   If it's already on, does it turn off and if so, when does it revert back to sensor control?  What if you throw the switch in the daylight?  You're pretty much at the mercy of the motion sensor to define what that does, and it may not be what you want.  

If you need better motion sensor coverage, that can be had by configuring multiple motion sensors.  That, however, requires neutral to the sensors and 2 hot wires between them.  

Daylight sensor.

Not turning on during daylight is one of the most basic functions of an exterior motion sensor. That feature is not as common with an interior sensor, but it should Just Work, you shouldn't have to tell it twice.   

That said, the better daylight sensors have to "learn" what daylight is. Consider sensor A, directly under a streetlight illuminating white concrete, and sensor B which is deep in the back of a carport: Sensor A may see more light at night than sensor B sees by day.  As such, both sensors need to "learn" what a day-night cycle looks like, for them. They have internal clocks and memory, and record hour-by-hour luminance averages over several days, and figure out which hours are dimmest.  I bought a cheapie Christmas tree light controller and installed it on a dim porch, first day, it ran the lights all day.  By day 3 it had figured out what "night" was.

Trouble is, when you cut power to one, it loses its memory and starts over.  That can happen from experimenting, or a miswired 3-way switch, or an upstream timer shutting it off.  

TLDR: give your motion sensor 3 days uninterrupted to get oriented to what "night" is.  If it still doesn't work, get a better one, perhaps one listed for exterior use, and perhaps one made to take neutral if you have that.  

Neutral

If you have access to neutral, consider using sensors that use neutral.  These wire very simply: aside from ground and neutral, they take an "always hot" connection and a "switched hot" connection like a plain switch. They have a guaranteed always-on power supply (via always-hot and neutral) so they remember... And since they're not leaking power through the bulb, they work fine with any bulb type.  Simply put, neutral-using sensors are better in every respect.  You can parallel several sensors or switches; if any is on, the lights are on. Between power supply and your last sensor, you need 2 hots and a neutral (14/3 wire).

LED

With 8 lights, you are pushing the capacity limits of many sensor switches unless you use LED.  I recommend you do. Price and selection is quite good now.  However many non-neutral sensors don't play well with an all-LED circuit. The workaround is to leave one incandescent in the circuit... which works until it burns out, which they frequently do... So use two.