You could perhaps ask her if it would be easier for her if your grandson came to your place on the days that she is working at home.
If she accepts, the problem is solved, if not you will need to try to accept that as Jaycee suggested that your DIL is not being rude when she is "mooching about" but concentrating on her work.,
And no, it is definitely not crazy that she won't collect him on the days she is working at home. She is WORKING and it is quite immaterial that she is doing so in her own home. She needs to concentrate on her work and neither have to break off to collect her son, or to wonder what he is doing while she is working.
Please try to re-read what you have written. What advice would you give someone who wrote the same about her DIL?
I know, we all do, that the mother-in-law daughter-in-law relationship is more often difficult than not, but could you try to accept that you and she may just have got off on the wrong foot? Make a list of her good points, you mentioned her bad ones, but didn't give examples, so it is difficult to know whether you are justified in feeling as you do, or not.
It is possible to read your post and feel that you DIL probably feels that you took an unreasonable dislike to her when first you met. If that is what she feels, she is actually trying to make an effort by letting you see the children. You feel she dislikes you, could you both be mistaken?