Congrats on the new little one on the way!
If you are starting LHTH at 3 are you planning for it to take a while to complete? I started it when my DD was 3 and we school 4 days a week, and the 3YO doesn't do school whenever there is any other conflict, or I have a lot on my plate, or her little brother is sick (aside from her being sick, me being sick, etc). Now it looks like it will last us until she is 5. Then she will get some time off and probably start LHFHG next fall. She has other activities she does for "school." Just because she wants to.
Beyond or LHFHG, if you have done them before, are super easy to add in. At least I think they are. Doing Bigger with LHFHG is challenging mainly from the perspective that both of them really need you for the whole thing, and Bigger takes a little chunk of time. I go back and forth, start with the oldest, then do all of Beyond (LHTH if my oldest takes a while with her stuff), then come back to my oldest, maybe after lunch if it's taking that long. If LHTH doesn't get done beforehand, I try to do it around 1 PM, after the 1YO goes down for his nap and before the 4YO has her rest time in her room. It is a nice little one-on-one time with her.
I don't know if you have had to school with a baby before, but I find it easier to school with a newborn up to about 10 months than a toddler! Babies sleep so much! My son is nearing 2 now and it is starting to get easier because there is a greater number of things he will do by himself now.
I hope this helps! You can do it, with God's help and enabling.
Doing Beyond and LHTH has worked good this year.... but how do you make it work with 3??... I think (hope) it is doable, but would like to know how to make it run smoothly.. at least on most days.