It always saddens me when I hear of paternal GPs being treated in this manner, and being made to feel this way. We all know that DDs generally gravitate towards their own parents, and that's fine. Most of us are, after all, DiLs ourselves and have been through it all before. This is not something new to present day mums.
Unless there's been relationship issues between a DiL, and MiL, previously, I can't understand why some DiLs deliberately make their husband's parents feel this way. There's no reason for making a GP, who isn't overstepping the mark, feel that they are not welcome, or they can't even have a little playtime, or read a book with their GC. It's very upsetting for any GP to be treated this way, if there is no valid reason.
Is your son present when you visit? If not, could it be that your DiL feels a little awkward/uncomfortable having you around when he's not there? I'd also appreciate the fact that they are both working, and have less time at home together with their little one. Someone did mention that a 1.5 hour visit, on your DiLs day off, may not be something she's happy with, but she's not stopped you from visiting, and understandably the little one will be needing her regular nap at some point.
Personally, I agree with whoever said that it's best for you to have a little word with your DiL and not your son, as you quite rightly said that he will simply tell his wife, and frankly, I think that will just get her back up, and make matters worse. There's no reason to be accusatory at all. Just be nice, and casually say that you hope she doesn't feel you're overstepping the mark with your visits, as you do understand how busy they are with work, etc. You could even casually, with a little laugh, say you don't mind doing the odd bit of housework/ironing/cooking, if it would help her out at all. That would mean less time for you with your GD, but it could help to ingratiate yourself to your DiL (even if she wouldn't dream of taking you up on the offer!), and help to improve/build upon your relationship with her. She doesn't have to take the offer literally, but she'll know you're thinking of her, and she'll probably sense that you are feeling a little unwelcome. Just tread carefully.
The issue with the gifts does sound rather rude, petty and unappreciative, not to let your GD play with them (assuming they are age appropriate, and adhere to safety regulations). My son has recently mentioned that they would like me to buy more wooden/fabric toys for my little GD, but I have been guilty of buying her the odd, 'all singing, all dancing, lights flashing', toys in the past ... just because!
However, I do now always ask what they would like me to for birthday/Christmas presents, as I realise that parents have their own ideas, and I prefer to buy things that they actually want her to have.
It's a shame about the situation at your son's birthday lunch, it must've made for a bit of an awkward atmosphere. It's still early days, and maybe your DiL is simply a bit over anxious. Hopefully, given time, she will relax a little, and you'll be able to enjoy the time that you do get to spend with your GD.
Don't try to rush the issue. Remain calm, casual, and polite at all times. There will no doubt be a time when they need you, and they'll let you know.