Age increases your risk.
I had GD for my fifth baby, born when I was almost 37. I had two babies who clocked in at 8.15 and 9.4 previously, and one who was 8.9 and first was 7.5. Did the test each time, and passed, but for the fifth, came up positive. I didn't do anything differently and my pre pregnancy BMI was well within the acceptable range. DC5 ended up weighing in at 9.1, so second biggest. The measurements are not likely to be just weight or air.
I brought three DCs with me for a lot of my prenatal visits when pg with DC5, including the glucose test, which was long and started early. I brought snacks and small toys for them. They ran riot in the waiting room and all I could do was sit tight and say 'this too shall pass'. They also came to the scan in a clinic a good way from home where DC5 was checked for Downs (I opted against amnio).
I controlled the GD with a very strict diabetes diet and regular blood sugar testing throughout the day but if I hadn't been able to do that I would have had to go on to insulin injections. It really isn't something that can be ignored if it's positive, and it really is something that needs to be tested for, so please exercise your right to turn down a test very judiciously.
I had to be induced right on her due date as the placenta can lose efficiency in late pregnancy with GD and the baby can be jeopardised if not delivered at 40 weeks at the latest.
I think I can see where the health team could get the idea that you are opposed to the test and are quite gung ho about this. It is possible they would think 'where there's a will there's a way' when it comes to childcare. Did you tell them about (1) just moving house and DD having tonsils out all in the same week (2) difficulty of arranging childcare for your DD and DS? If you focused on medical aspects of the question, seemed anti-hospital, and questioned whether the test was medically necessary when they seem to think it is, then they are going to draw the conclusion they have drawn. Have you asked them about on-site childcare facilities?
Babies of mothers with GD may experience:
shoulder dystocia during delivery (home birth not a good idea)
high birth weight
respiratory distress
low blood sugar which can lead to seizures
mineral imbalances requiring intervention
jaundice
future type 2 diabetes
death
You yourself may experience:
emergency c-section
high blood pressure
pre-eclampsia and eclampsia
future type 2 diabetes
Although you are stressed up to your eyeballs, your diet of McDs and chocolate will have to change whether you have GD or not. Please try to get a handle on the stress and try not to let present problems overwhelm you to the point where you lose sight of important longer term priorities such as your own health and the health of the baby.