The only advice you need is to be as honest and as forthright as you can be. The girl needs to let you know what her real situation is with her boyfriend, and IF she is already as a crossroads in their relationship you may want to let her know how you feel about her. If she is really through with her boyfriend that is one thing, but if she is still in a realationship or if she is ambivialent that is something else.
Remember there is also the question of the 9 year old son’s father. Is he still in the picture OR is he the son of the former boyfriend. How do you or how will you get along with her son ? Does the son have visiting rights with his father ?
The girl may have a problem keeping a relationship going. What is it that happened with the boys father ? Was she married to him before, if she was, now you have the problem of her having to get an annulment through the Church.
There are a host of problems with this potential relationship, all of which you have to have answers for if you are to even consider making it last.
It is going to take a lot of patience and a lot of hard work on both your parts to make this thing work. SO far you sound like you may be willing to put the effort into making it happen, but you need the girl (and probably her son) to have the same commitment and energy and patience to even get it off the ground.
My guess is that the girl probably has a few similar feelings towards you also as she spent some time with you on the vacation (otherwise she would have just told you to get lost. Most people do not strike up a relationship with perfect strangers)
You need to get into very serious discussions with the girl, and find out how she really feels, and find out if you even have a chance to make work. Plus the discusion have to ongoing and consistent. The key to any successful relationship is communications.
IF she can not speak to you now, or she can not determine for certain, how she feels about you or her boyfriend then you are sunk from the start.
It may be that she is the type of person who has problems making long term commitments. It takes two to make a relationship last, so far you only have one.
IF I were in your position I would look elsewhere, but if you do move forward with this, be very careful and make very sure the girl feels as committed to making the relationship last and permanent as you do.
Down the road if she is later ambivalent towards you, she may take up with yet another guy, as she may with you. Afterall she has already left one guy with whom she had a son, and now she is looking to leave another one.