Hi LilahRose
That you're feeling like a ghastly mother is a strong indicator that you aren't one. Your life does sound overwhelming, though, and you deserve a huge amount of credit for just getting our of bed each morning, let alone for starting up in this program!
Raising children takes enormous energy and patience and it's definitely not a bad thing for you to want time and space for yourself. My ex and I split up when my girls were 4 and 6, and there were times when I thought I would go mad if I didn't get away from them. They are 11 and 13 now, and it's only within the past couple of years that I've been able to have a complete thought when they are around me. Your husband just left you a few months ago -- as well as dealing with the emotional turmoil of how he treated you, you must also be in a panic about how you are going to be able to support your children and yourself on your own. To have your kids around you, incessantly wanting you, loving you, needing you (hating you, yelling at you and whining at you, too, probably, if I'm to be realistic) when you really need to think and plan can be suffocating. And all the everyday things that kids need -- especially if yours are not at school yet -- meals, snacks, drinks, clean clothes, stories, attention, etc, etc, etc! It's tough to handle in the best frame of mind, so please, please be kind to yourself for finding it tough right now!
You obviously love your children deeply to be so concerned about the impact your panic, depression and withdrawal may have on them. That love is the most important thing they need. Even if you believe that someone else could provide them with the patience, the home-cooked meals, the range of activities that are supposed to be ideal for developing a well-balanced young adult -- it still wouldn't be as good for them as your love.
Getting some time for yourself is pretty critical, though. A babysitter or daycare once or twice a week? If funds are tight, there may be family or community services around that could give you a break. Nobody is going to think the worse of you for saying that you need a few hours away from your children. The opposite, I would think -- knowing when you are close to your limit and asking for help before you actually cross it shows how strong,