I think you need to have a frank discussion with your father-in-law about your expectations, and really listen to his answers. I don't know how old he is, but maybe he is just too tired to deal with an energetic toddler. It might be very hard for him to face this reality. Instead of sending over information to him about things, tell him that you want him to take your daughter to such-and-such activity. If he doesn't take her, ask why. If you notice her diaper is soaking when you pick her up, point it out and let him know that he needs to check her diaper more frequently so she doesn't get diaper rash. (Or if he's up for it, he can potty train her.) If being direct and clear with him about what you want doesn't help, then I think it would be reasonable for you to enroll your little one in preschool or some other kind of care, even if it's just part-time. If you are worried about offending him, you could tell him that you really want him to have a great relationship with his grandkids, and you feel like giving him a break will allow him to be more energetic during the times they're together.
I think with regard to your older daughter, you may want to find after-school programs for her. However, I do think it's important that she understands respect for her grandfather. True, she will not always agree with what he has to say, but she also needs to acknowledge and accept that he was raised in an era when children did not speak to adults until adults spoke to them, and children addressed adults as "ma'am" and "sir." There's nothing wrong with your daughter having her opinions, however there is much to be said for learning to keep them to herself, and understanding that everybody in the world is not always interested in what pre-teens have to say about everything. Shutting one's mouth at strategic moments is a skill that comes in very handy at work, so it is not a wasted skill for her to learn now! =)
As far as telecommuting goes, I've been down that road and it can be a very good thing for a working mom. You are a bit more flexible to attend school events, pick them up from school, etc. However, don't assume that you will be able to watch your toddler while telecommuting. You still have a job to do, and kids are a full time job unto themselves. When my kids were that age, I had a nanny so I could still attend meetings, travel, go into the office, etc, and she kept them entertained and busy all day. I will say that if you do telecommute, make sure you have an actual office in your house, complete with locking door. I recall several instances where my kids would literally be hurling themselves against my office door while I was on the phone with clients... kids don't really understand why you're on the phone and can't drop everything to attend to their skinned knee or look at the snail they found or whatever. You still need a responsible adult to watch them while you're working.
Good luck with everything. It's really, really hard to work full time with kids. It doesn't really get easier as they get older, at least not from what I've found. Ugh! I feel your pain.