K. - Sorry to hear you are going through a tough time right now. I have a girl who is 3 today, and also a 3 month old baby, so a little similar to you. And Daddy has been recently working out of town for 1/2 weeks at his new job, which is new for our family. When he started being away for multiple days, my 3 yr old would also ask me to lay by her at bedtime, which I never would do before (hubby sometimes did that before). Sometimes I do it, because I feel that she does get stressed/sad with him gone, and needs a little TLC. Sometimes I don't do it, especially if I tell her something like, "Your sister needs me now" or "I need to finish sending the email to Daddy to tell about our day," and she is okay w/it.
My daughter has traditionally always gotten up at 0630 and to bed at 10:30pm, and now with summer naps 2-4hours. (I am now trying to shift some of her daytime sleep to nitetime sleep, if it works is yet to be determined!) If we go to the park for a couple of hours daily, this usually tires her out to go to sleep, so make sure dd is getting enough activity. Otherwise, it is okay for them to lay in bed w/some toys, talk, play a little; anticipating this, I've been offering a specific toy just for nap time to get her to lay down. I also have a specific lullabye CD for naptime, and one for bedtime, that plays after I've left. This is what works for us.
Best of luck for you! I know it is difficult to go the entire day with no respite. I take my "me time" when they both nap in the afternoon. Hope you find something that works for you!
T.