There is no guarantee that this woman is going to be around in 2016 or her mental facilities will still be good. If the house continues to go down hill, when it comes to purchase the home, you may not be able to get a loan for it because of all the issues. How old is the house? What is the condition of the rest of the house that you aren't renting? What's to say that there isn't lead paint under the current layers of paint, iron pipes, the plumbing may need to be brought up to code, electrical wiring will probably need to be brought up to code, and is there a possibility of asbestos in the home, what's the condition of the outside of the home? These are all considerations that you will need to take into account if this is something you truly want and all of them are big ticket money items. Are you going to be willing to take all of this on?
I would draft up a letter w/what needs to be repaired and send it to her certified mail/return receipt. I would state that the repairs need to be done and if she can't oversee them, then you would be more than willing to have someone come in and pay for them, with the understanding that the amount would be deducted from that month's rent. No one should have to live like that. It's not healthy for you or your children. As for the light not working, it could be a cause for concern, i.e., frayed wiring, switch issue, mouse nibble on the wires or water has been dripping and shorted it out...but no matter what, it's something that needs to be fixed.
Have the gaps in the floor boards been there forever or just happened?
Sorry to ramble on, but you have some issues that duct tape and wood glue aren't going to fix. She needs to cough up some money and have these things repaired asap.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.