I can't tell you how many times that both my mom and my dad were near death's door for years before they passed. I went there often, driving the two hour round trip even knowing it was hard for me with the MS and the stress.
I voted for you to stick by the phone and hope for the best. If she does really take a turn for the worse you can make the flight and just pay more for a short notice flight. Since your own health has been so poor lately it will be best for all involved if you stick to home until if/when you really need to go.
Then, if you must, stay at a hotel and only visit briefly so you can get home to rest and little Jack.
Of course this is only my opinion and you should follow your own heart. Whatever you decide it will be ok.