I have had the tendancy in the past to be a people pleaser and feel guilty easily if a friend was in need. All changes when you get married and/or have children. You pretty much answered your own question.
When things become challenging moms will find a way to make things work, just as you are having to do she will too. Just tell her you are sorry and repeat what you just told us. Just don't over apologize since you too have a family that depends on you.
"My vehicle is not large enough to have 3 carseats and a school age child in it all at one time."
" was becoming stressed out about my family's financial issues."
"I am stupid if I don't take the position which has a LOT of potential for advancement and benefits."
"I have a baby/toddler which I am going to have to place in daycare."