Who can do them? My daughters in gymnastics can do them like they are going out of style? I tried one the other day and I couldn’t even lift my legs (legs are straight) halfway up. What area of my body is lacking in the strength to keep my legs raised halfway up?
Are you able to do knee raises? That is usually the scaled down alternative. It most likely your abs that are lacking but due to the hanging you use almost all of your upper body during that movement. Also remember that because you are (probably) taller and heavier than your daughter your legs are longer and heavier. This makes it much harder to lift them because your legs are further away from your body. However, I’ve been doing them for a while and can do at least 12 no problem. It’s usually my grip that gives out before my abs do.
I can do hanging knee raises about 15-20. Do I start out trying to keep my legs straight out in front of me?
I can do hanging knee raises about 15-20 but then I’m out of breath until half past 
There are probably a couple of ways to work up to straight legs. If you can only do a couple then I would do as many straight leg as you can and then finish the set with knee raises. You could also start doing the knee raises while holding a 5 or 10 lb dumbell (or other weight) between your feet until you are strong enough to do the straight leg.
Also, don’t forget that other ab exercises will also help you get to the goal of straight leg raises. So just work at getting an overall stronger core and the leg raises will come along with it.
Start out by doing knee lifts. You dont even need to be hanging or on any type of devise, just stand and lift your knee up to your chest and then switch and do the other, as you’re doing them also start raising your arms and hands above your head with each knee lift. walk around as you’re doing them, you don’t need to stay in one spot either. Do some at a slower pace, then pick up the tempo and pump a few out at a faster pace. These are good for your abs and core which is needed and also the upper part of your leg ( soas and sartorius ) and all those wild muscles around the groin.
You want to be able to do these all day. But itll probably suck for you after only doing a set of say 10 each leg. But this little movement is good for you.
After a while, get into the leg raises again, if you cant even lift half way then do sets of 8 or so lifting only 1/4 of the way up. You may have to go a full month only doing 1/4 lifts,
Do these a few times a week randomly, sets of 8 reps , 3 or so sets. No need to be super specific with numbers or count. Do them, take a break, do some more. Mini movements.
Then after a few weeks, see if you can do one full one, you may even be able to get 2.
There is also a lot of upper body involved with the hanging movement. Dont know how many chin ups you can do but if you cant do any, then hang from that same bar and work on pulling yourself only 1/4 of the way up for sets of 5 to 10 reps. Get your body used to pulling your weight. Do those frequently.
Combine a bunch of those 1/4 movements together after about a month, along with some knee lifts and you may get that 1 full leg raiser in no time.