The baby is still very young and this "Bonding" that you talk of wanting to happen is what happens with the parents (or primary care giver) so please don't get out of shape about that.
Feelings of jealousy are just that "feelings" they are yours and you can let them grow by perpetuating your "belief" that you are being the "Victim" of some unfair treatment.
OR - or you can change your 'Thinking" and give yourself a new Message.
Up to you.
Your new self message could be something along the lines of ' we see this Baby when we do AND we will be seeing a Small Person growing up'.
As Covid passes and we have more time, we will see her more. As the NEW parents to a NEW baby become parents to a toddler, a teenager and so on WE WILL be there. We are apart of this child's life as much as the other GP's. We will find our place.
You say the other GP's are retired and reasonably well off while your and your OH are still working and that brings other factors into the situation. If other GM can settle baby and you can't maybe it has to do with other things besides being there more.
Factors such as she is DiL's mum so will "Feel" to baby more familiar, she hasn't had to drive to get there, hasn't been at work, isn't trying to "Fit a visit in" ergo she isn't as tense or stressed as you - most naturally you won't feel as relaxed as other GM and these things transmit, especially to very young babies.
Asking to visit and not being allowed - hummm - that's an other issue. Change your question. IF I read your post correctly you are saying to DS "I have xx time and I want to come visit. Nothing really wrong in that but it isn't working for you.
Ask instead WHEN , for how long, continue to offer to stay in a hotel. Don't even go there for asking to do parenting jobs such as bath time.
You can make the long term situation better OR you can make it worse. But if you are asking for help you clearly Don't want to make it worse.
It's hard on you and it's a tough place to be so well done you for reaching out.
Are the other GP's getting a better shot at being GP's than you are ? Yep.
They probably are. That's a hard to take but if you're in this for the long haul you take it.
Are your DS and Dil including her parents more in their family life than they are including you? Yep. They probably are. Again tough to take.
Your DS and DiL are new at this parenting lark too so it's up to you to be the more giving person, it's hard on you and your feeling hurt but it is what it is so softly, softly is probably your best way forward.
Also your son is probably just going along with what his wife wants and what feels easy, less stress.
I know I set the family patterns and so did my friends, it's also what I see with my DD and with DD's of my friends families. Son's seem to hand over certain bit's of family responsibilities to we Women Folk.
If this helps we have a 9yr old GD, she was born in New Zealand and I was there for 3 months to cover before she was born and 6 weeks after. Her other Gran couldn't be there, DH and I went for 3 weeks when she was 6 months old, other Gran couldn't be there. DD and SiL came back to UK when DGD was 14 months old and lived with us for 8 months until there stuff got here. They went to see other Gran a couple of times in those 8 months. Since then they probably see SiL's Mum 6 times a year, we live closer and until Covid have gone to there's most weeks. So as you can see we have had lots more contact with DGD than other Gran, it's just the way life is. I like other Gran but she lives down south and no longer drives due to eye sight.
However, DGD knows other Gran well, loves her very much, we talk about what they do together when she sees other Gran and we play with new toys she's had from other Gran. She does the reverse with Gran re us because she tells us. DGD knows us all, doesn't really remember her other Grandad as she was only 2 and a bit when he died but talks about him when we look a pictures.
So for some children building GP relationships it isn't always about frequency of contact. It's about letting all the members of their extended family be part of their inner world as much as being there in their outer world.
I'm sad you're feeling hurt, I always feel for DGD's other Gran as she is on her own and I know she misses DGD and her son very much but life is what it is and we do the best we can. good Luck and I hope you have found some helpful suggestions on GN.