Alternating Upper and Lower strength Training

I do upper/lower splits but I've been lifting off and on for over 15 years; consistently the last 14 mths after a 2 year break. It is what works for me after all the different variations I've done. Newbies are more encouraged to start with full body workouts and move on from there but a U/L can be just as effective as your hitting both areas twice a week.

As a beginner don't worry about an upper/lower split yet. Do full body, if you only have 2 days a week to do it, that's fine. Then as the weights get heavier and you get more experienced, you'll need more time to recover, so a 2 day a week split like you posted will work. When I was powerlifting I'd only do 2 days a week, one day would be oriented around bench, then the other workout would be squat/deadlift centric. Usually Monday and then Thursday for workout days to allow plenty of recovery time.

yep and give your self periods of rest for muscle repair. Most body builders today do a 6 day cycle focusing on each muscle only once duringthe cycle.

my routine: Upper, Cardio, Lower, Cardio, Yoga, Rest.... start over.

Depending on your recovery capacity and the intensity of your workouts, Your 'upper' day could be rest for your 'lower' day and vice versa.

The point I'd like to add is make sure you're hitting your whole body.

A good upper body workout should have at least one vertical push (ex overhead press) one vertical pull (ex pullups) one horizontal push (ex bench press) and one horizontal pull (ex rows). Also helpful would be one inverted push (ex dips) and one inverted pull (ex shrugs). I like doing arm stuff because I'm vain, but if you're pressed for time the stuff listed above should take priority. That's also not including stuff targetting smaller musculature (ex cuff work) for prehab/rehab or variations on the basic movement (ex DB movements instead of barbell to account for strength imbalances in the arms). This makes for a pretty darn long session to get through at once (I'm not saying you have to do all of this stuff, the big movements should be the bread and butter but you shouldn't out of hand disregard the other stuff).

A good lower body workout should have a quad dominant exercise (ex Squats) and a hamstring dominant exercise (ex Deadlift). Other things that would be nice would be calf work (ex Calf Raises) and targeted lower back work if you didn't do that on your upper body day (ex Good Mornings). There's also ab work if you didn't do it on your upper body day (ex Ab Wheel). You also have the prehab/rehab and variation options, similar to those with upper body work. The other thing with lower body work that I've found helped me a lot is volume. Nothing upped my squat like doing lots and lots of squatting. I think lots of volume is important for leg work, particularly the squat side. That makes lower body day ALSO a potentially huge time sink.

I love UL splits, but unfortunately I can only really do them when I have large blocks of time at the gym to dedicate to them. Since I don't I've modified my plans slightly. I basically do a similar thing to Gallow. Other folks do full body workouts, which can be useful particularly if you're a beginner (though I tend to think those should be supplemented with some accessory work, that's my own personal bias).

Whatever you do make sure you get a complete workout over your training cycles, it'll help you in the long run.