Stoves are pretty simple devices with only three ways to control them;
1: Air in
2: Fuel
3: Air out
By the sounds of your stove, I would say number three is hardly the issue as that is really just draft control of the chimney. Number two may be your issue, but only if you are using super dry wood that was felled, split and stored many years ago, but then again, I doubt that is the issue either. This ultimately leads me to the first issue which is air in. Unless you can seal off the intake air with positive draft controls on the
ash pan cover, fire box cover and any external draft controls; you are not going to control the fire and go through a lot of wood. The fact that you can see into the firebox is a real problem.
Consider this; as long as you have good draft going up the chimney, the least of your problems will be consumption of wood. That is the air is going INTO these points and not coming OUT Of them.
Should you lose draft like on a damp and foggy day; there is a possibility that smoke will come out of those points if you are truly lucky, and carbon monoxide if you aren't.
I think you can see where I am going with this. That stove is not safe to operate! I am not trying to break your bubble, I am not trying to be mean, And I am not trying to post a negative post; I'm telling you straight up it could kill you if the right atmospheric conditions present itself.
Can you fix it? Only you can determine that by honestly assessing your skills. Myself, I weld battleships together for the US Navy in my real job, but even I find welding
cast iron difficult. Obviously steel I have no issue welding, and I am proficient with shears and a pop rivet gun on some shielding stuff, and I have modified and fixed many stoves. Still...sometimes they just cannot be fixed.
There are many, many good used stoves out there if acquiring one is an issue fiscally. Maybe there is a way to barter? I really, really, really would consider an alternative to that one. I have not seen it, and could not assess it from a picture, but my intuition thinks that it may be beyond the hope of repair. Until it is fixed, for the sake of yourself, your husband, and children perhaps; do not risk your lives operating that stove.