baddy that sounds really tough :( Your DD1 will be stressed by a new baby no matter how you feed her. It's usually a challenge when a new baby comes along, no matter the age of the sibling, and it can be so hard when you're trying to figure out the new baby thing while juggling a toddler's needs.
That sensation of feeling overwhelmed by being the only person who can feed your baby is felt by most mums and it's really intense at the beginning. I can say that it will pass, if you can work through it. As breastfeeding gets easier and you can do stuff at the same time as feeding there's the advantage that you can feed with both hands free, or in a sling, which can make toddler management much easier. No hot water to worry about, and no time taken away from the toddler to make up feeds...
Someone once pointed out that right now the baby needed her, and her toddler wanted her. There's quite a difference between the two. You sound like a very responsive parent who feels guilty about leaving her older child without the attention she wants and deserves, and that's such a lot of pressure. Can you possibly find anyone to help for a few weeks so you can get through the first, intense breastfeeding weeks when things will be much easier?
Breastfeedingis important and the health implications are significant, so it really is worth trying to find a path through which balances the needs of everyone - even if the balance can't be found for another 3 or 4 weeks. Sadly your little one can't possibly understand that, and you are the only trying to help her through this big transition, and that's sooo tough.
You haven't stressed out your DD2. It's inevitable, just as it's inevitable that she will come to terms with things. CBeebies is ok for a few weeks :) or whatever will distract her. She will be fine, and she will learn about breastfeeding, nurturing and the importance of it all first hand which will in turn help her when her time comes, progressing the cycle of health which you have started.
I hope tomorrow goes better xx