@docmrm Yes, you can do it - mind over matter!
3 hour flight will actually go by very quickly - dress baby in pyjamas and do normal bedtime routine ahead of taking the flight whilst you are at the airport. Get to the airport early, do dinner at the airport, allow for time in playspace (if you live in the UK this is a pre-flight ritual for my kids at Heathrow and Gatwick!)
For the three year old, bring snacks - I find starch based snacks like cheerios/crackers/breadsticks work best, allow a few shows on the ipad, sticker books, they probably will fall asleep more easily than you think.
Be prepared that the ride to your final destination is probably going to be the hardest part - enlist your family to meet you at the airport, help with transportation, and help with the kids.
I've taken multiple solo flights - key is to just bring extra clothes (for everyone) get there early, expect that things won't go as planned, and bring nice fancy snacks for yourself (I always pack a fancy bar of chocolate just for me!)