Our first helper had some issues but she was good at cleaning and a few things but she wasn't good with kids and at the end of the day, that's her primary responsibility. It doesn't matter if my house isn't that clean or the food we eat isn't gourmet-level. It does matter how my helper interacts with my kids. In the case of her ignoring your son and choosing to not interact with him, I would say that's a huge problem--especially if she's spending large amounts of time with your children--those little things can really affect the way a child sees himself.
Y'know, when I was in secondary school I babysat a lot. Guess what? Like Elle, I didn't really feel comfortable around kids. Of course, I didn't have kids of my own and at that point I told myself I would never, ever have kids. I wasn't particularly interested in children either--like all my friends would be "ooohing" and "ahhing" when they saw a cute baby and I would have absolutely no reaction at all. Y'know what I did? I prentended. I acted. I babysat because I wanted to earn extra money. I was responsible and could handle children but it totally didn't come naturally to me. It was actually really boring and wearying taking care of kids. If I had had the option to do another part-time job to earn funds (like McDonald's but our town definitely didn't have one of them) I certainly would have done it. Some of the children I babysat were well-behaved and some were terrors but I didn't enjoy being a babysitter, actually. But, I was really, really, really good at it. In fact, I was so good at it that my name "got around" and I would be getting multiple calls during a week, "Hello. My friend mentioned that you've done some babysitting for their children and that you do such an excellent job. Do you have any time to babysit for us?" I even had one many comment, "I just saw you interacting with that child and thought 'Wow, she's really a natural.'" Was I really a natural? Not really. It was part of my job and I wanted to do a good job so I learned "the tricks" that worked for me to handle little (and older) kids. And I was open to suggestion--just like you have made so many suggestions to your helper.
Like the director of a helper agency told me when I shared my issues with our old helper (whom we had been trying to encourage to change for 3 months), "Sometimes some people aren't going to learn. You could talk and try to teach and demonstrate but it's beyond their scope to learn for whatever reason." It may come down to you having to accept that she's not going to take up your advice and learn (if she hasn't in a year, obviously, there is something wrong). And you just have to decide if it's okay for her to be like that.
For me, it wouldn't be. Because, like I said, interacting with my children and having a relationship with them is part of my helper's job--it's actually her primary job. And you have said "she didn't do anything wrong"--I disagree. I think that if an employer comes to you earnestly and says, "It is really important that you build a relationship with my kids and these are the things I want you to do" and then the helper does absolutely nothing with this information or plea--I think that is inexcusable. If my boss said the same to me and I did nothing, that would be grounds for firing, I think. It seems, your helper, like our previous helper, is not working up to standard in a very important area.
The only other thing I could suggest is to actually time-table and "force" her to do the things you have previously suggested. Make her accountable. Consider it professional development or on-the-job-training. Like, on Mondays it is baking day and this is what you are going to do with the children. I will expect a report on how it went. On Tuesday it is park day and you are going to take the children to the park and then I will ask them later what games they played with you. Your options for games are this, this or that. The kids and I will demonstrate to you how to play them. Etc. Etc.
Or, maybe light a fire under her and tell her that you're not pleased with her attitude toward your children. I dunno...to me, it would be a big deal but that's because my helper spends a lot of time with my children and I want to make sure the message she is sending with her behavior is that they are wanted and loved...not a nuisance or outside of her area of interest.
