Women aren’t required to do mitzvos that are ‘timed.’ Yet women are supposed to daven before they do their household chores. How can a mother of several kids do that? I, myself, only have 3 teens at home but I have to get up at 6:30 am to ready the breakfasts & pack the lunches to go, sometimes empty the dishwasher or do the dishes that are in the sink from post dinner snacks (teens stay up later than their parents) & gather dirty laundry & start the 1st of the several loads of laundry.
Then I drive a car pool. Come home & do up the dishes from breakfast & drive another car pool. Sometimes, it’s 10:30 am before I can eat breakfast. I’m 63 years old. You’re supposed to eat breakfast within 2 hours of waking. So do I daven first or eat breakfast? There’s just so much guilt pressing on me to daven as early as possible but it’s just impossible most days.
There is no need for you to daven the entire davening before you do all of these activities. Before you eat, you should say the beginning of davening, up to and including Birkos Ha-Torah. After this, you can eat, as well as do all the necessary chores, and then complete the davening. Mothers with young children almost invariable daven after they complete the things they need to take care of (the especially devout rise early and daven before, but this is rare). There is nothing wrong with this.
In general, you certainly shouldn’t have feelings of guilt over this and similar matters. Halachah does not go “against” the individual, but rather “with” him, and davening (or other elements of avodas Hashem) ought not to hinder your life, but to enhance it.