I have heard that you can fly up to 36 weeks, I also travel a lot for work and luckily my boss has said that i should minimise this (gosh so often i realise how lucky i am with my employer, also a big corporate - i currently work mainly from home and this will continue when i get back to work). so now i go when i need to and when i think i can handle it. I used to travel internationally around 60% of the time and there is no way i could do that, now it is domestic and even that is tiring at my early stage.
I think you need to set some ground rules. there are so many options to work virtually that travel should not be so necessary and they shld not push yu extra hard in the lead up to your mat leave. they also should not hold out 'carrots' to you, they need to decide what they can offer you and then commit to it.
It sounds like you know whats important, and that is you and the baby at this point. sit down and have a good chat to your boss - i am sure you will feel better for it and if you dont ask you dont get.