good on you for getting most of your ducks in a row right off. your tracking will pay off later.
If I were you and I wanted to drop 50 lbs. Id just do keto, get nice a settled in on it and go cruise control.
One reason I say this is that is works, keto will make you drop weight and two if you cant workout regularly you wont be able to get that burn going.
Now if you do not want to do keto, only eat your carbs after your workout. you will have to find out how many you really need and this may depend on the workout for the day.
These are just going to be used for glycogen replenishment. You need to get them from good sources not like birthday cake etc.
. Vegetables are your friend here.
drink the heck out of some water too. If you arent tracking your meals, start it right now. Plan them out in advance. you can still make progress, albeit small, on a deficit. I dropped 1k calories and still managed to put +10 lbs on my bench 1RM.
I completely understand the trying to workout around kids thing. I literally put 2 down for a nap, get to the basement and get to work. I dont always get done before they wake up but typically I do.
you are just going to have to plan ahead and find the best time. Home gym was the best thing for me. I can listen to what music I want and dont have to leave the house. Dont forget about simple things you can do
at home to at least have some progress when you cant hit the gym. all different push up variants, chin ups, plank, get creative! Just think activity = burn and that is what you want.
Also, starting strength/5x5 etc programs arent always ideal for weight loss. If it were me you need to add in something at the end that keeps your heart at a steady rate. This is calorie burn mode.
Lifting uses calories but its more of a rep 1, 2, 3, 4, 5 rest............ rep 1, 2, 3, 4, 5 rest........... Where as say kettle bell swings is just a constant engagement. make sense?