New Mom's Car Quit!

1st congrats on the new baby.

I would think you are looking at a possible fuel filter issue. Or perhaps a filter sock issue. (That's the screen that located in the fuel tank and helps to prevent sediment from actually getting into the fuel lines and making it to the filter)

usually on high mileage vehicles you have impurities that build up in the tank over time. As your fuel level gets lower the concentration of impurities becomes higher.

I would recommend changing the filter 1st its the cheapest and easier to do.

After that have a fuel pressure reading taken. This will tell you if your fuel is still limited and if you need to (a) seek a sock replacement.
(b) possibly if your fuel pump is getting weak.

My thought on why it started the next day is that as your vehicle sat the sediment in the filter had time to settle to the bottom of the filter. Once your vehicles fuel system pressurized you still had enough to maintain a flow but as the demand increases it become more restricted and starts to die due to fuel starvation.

Hopefully its just a filter and your up and running soon. I would also recommend running an fuel injection cleaner/additive thru your system just to be on the safe side and prevent possible issues further down the road.

If it doesnt please post a reply and I will starting asking some detailed questions to help you narrow down the issue.

Thanks
Roaming1