I have an 18 month old and we see my parents every 2 weeks and DPs parents every 3/4 weeks (he arranges it like that, not me). With working, toddler groups, visiting both sets of grandparents, siblings on both sides and friends, and trying to get some time out just us and DD, we are constantly busy. We just don't have more time. I suspect your son and DIL are the same. I think being some distance away makes it harder as well. My parents are over an hours drive away, we can't just pop in after work or school during the week.
I think you're overthinking it though. Some kids are just shy. DDs shy when she first sees anyone, be it her grandparents or the nursery staff she spends 3 days a week with. Its something he will probably grow out of, he won't be 10 and still shy when he first sees you.
But why did you feel the need to ask your DIL how often you should visit when your GS was first born? That would really put me off having someone visit, if they excepected a set visiting schedule. It's better to just go with it, see when you're all free, rather than expecting set visits.
Also, you say it must be easier with a daughters children but have just said your DILs mother sees the children less than you do, so that's obviously not always the case!