I was in a similar situation when I had dc2 as my parents had said they would have dc1 but booked a holiday a week before I was due to return 1 day before my due date.
To be honest it was stressful as we then needed to come up with an alternative plan. But Personally I've always been of the view that my kids are not my parents responsibility.
Its sometimes annoying when they agree to watch my kids (rarely) but then change their mind at the last minute, which happens most times they offer. We used to have to cancel or change plans so much at the last minute now we don't book anything and see it as a bonus if they dont cancel. But my mum has health problems too so I understand why she does cancel.
It sounds like your parents are doing their best to help both their children in a difficult situation. If you mum has problems lifting then she can't help your sister abroad so your dad needs to go, but has booked his return before your due date. You mum is right you don't need to do much lifting with a mobile 2 year old and she would cope alone if she needs to.
She would probably be upset if you got a childminder as you might make her feel like You only trust her with your dc when your father is around.
In reality you could have problems in labour or you could be home within a couple of hours.
You just have to make it work with your second, its always more of a struggle. We decided that if I went into labour when my parents were away my best friend would be my birthing partner and my dh would come straight up with dc1 afterwards.
We found changing birth partner was so much easier to organise than going down a child minder route. Yes its not ideal and its not what I wanted but I also didn't want to organise someone unfamiliar to care for dc1 and be worrying about him all the way through labour. (He has asd and a delayed swallow reflex so Struggles with food and has got some stuck in his airway before needing emergency surgery to remove it) Personally I couldn't have concentrated in labour with worrying about him if he had been left with someone who didn't know him and his needs.
I know this probably sounds harsh but when I was in your position I just decided I didn't NEED someone with me it was more a want. My dc1 did need someone with him. So if everything else fell through I would have to do it alone.
If youre planning on labouring at home as long as possible can you drop your dc of on route to reduce time your mum has him alone (if your dad is still away)?
Do yoy have a friend who would be willing to come to the hospital if your dh does need to go back?
I'm hope just like me though its just all theoretical and it works out that both your parents are home. Good luck with your labour and new baby