First, I do not think either of you are getting out of this relationship what you need/desire.
It seems to me she needs someone full time in her life and is in the bars looking for that since you are not there, I know this is very hard to accept as you feel you are giving it your all. Sometimes though you can give it your all and it is not enough.
The fact that your children have taken priority in your life is commendable, I have done the same for many years. But, there comes a time in your life where you also need to recongnise your own needs. I suppose that is what you have done by pursuing a relationship with this woman. I just do not think this is the best woman for you.
I am sure you both have a lot to offer to someone, but just not to each other. I think if you find that right woman you will not need to question intentions/motivations/feelings. Of course I myself dream of finding that perfect for me man so I may not be the best on this subject as I have yet to see that occur.
You may be best to let her go find her own way and you go yours so you can open yourself to a better experience. It sounds like you have a lot to give/offer to someone who appreciates it and someone you will allow in your life on a full time basis.
I understand that these type of long distance/partial relationships work for some people but I feel each of you wants more then the other can give.
I am no relationship expert by any means but I think you can find someone who will be more devoted and dedicated to you but you must also be willing to let them in.
I do hope you can either resolve this or find someone who better suits your needs.