This sounds very much like a combination of postpregnancy depression - a very real condition - & isolation/loneliness.
It isn't that you don't love your kids, it's that you are hormonally a mess, alone - you lack adult contact - kids just do not have the same communication skills as adults & they may be cute but they can also be boring (i mean how much interest can you build up re changing nappies!!) plus kids that young are extraordinarily demanding - my 2 are 9 & about to turn 16 & I still have trouble getting them to comprehend that I have a right to go to the toilet without interruption!!
You need to talk to your husband (is there anyone who can take the kids for a day so that you & he can really sit & talk without interruption because getting him to understand will be hard enough without interruptions from babies!!) explain to him how you feel, point out that he must have seen news stories about women depressed after having children,. Explain how isolated you are, how tired (you must be tired!!) how you lack adult contact & need to have some time away on a regular basis from the kids & that he needs to step up to the plate.
It's fine, great in fact that he (& you ) are doing all this wrok/study to build a life for yourselves & the kids but there's not alot of point if you get that at the risk of health, marriage etc. The etc is real, it doesn't just happen to others.
So 1) get someone to take kids so that you & husband can
2) really talk & work out some strategies like
3) time out regularly for you, with adults/friends/away from kids,
4) him taking somemore responsibility for the kids care
5) any chance of you getting a second car? Even being able to take the kids to playgroups, shops, visit friends etc would be a huge help & make it more easy to get them looked after if at times you just can not.
Good luck, also you could try things like: valerian, viatmin b, long hot baths (if the kids let you!!).