I wouldn't trust Jet Airways, even more so now since they are in financial difficulties. I would go EK, even with a stopover they've got quite a lot of flights both on BOM-DXB and DXB-LHR/LGW

Failing that, re assess your plan, do you know how long you will need to be in the hospital? Do you have friends/family here who can look after your kids here for couple of days while your wife goes to pick up your other child ?