I have two kids that are now 4 and 6, but they are about 2.5 years apart, like yours. Luckily, we never really watched much TV and I was quite adamant about our kids growing up pretty screen-free. It's so much easier to to not start than to stop some things. Now that they are both older, we pull out the TV about once a month for a family movie night. They don't get to play with our phones, laptops, or tablets. Instead they play with toys and read books, but that's all they've ever known.
DH and I watch TV probably most evenings on our laptop, after the kids are in bed. In a week we probably watch a total of 5-6 hours. So this is a relatively low level of TV time, but we are trying to stop that, actually. And it is kinda hard!
I would suggest first getting yourself away from it during naptimes, like others have suggested. (I always felt like I had chores that need done during naptime, but if not I like to read.)
For the kids, if you have a good baby carrier that can help a lot. I nursed on the go all the time when my youngest was born. There was no other way to do it with a 2-3 year old running around. I wore her a lot while she was nursing, and tried to get her in her crib for naps, which I was able to do most of the time. Give your older kid something specific to do if you really need to be left alone with the baby. It would really be a huge benefit to your toddler to have something enriching going on instead of being in front of the TV. It truly is damaging for young brains.
Since I still watch TV in the evenings with DH, I can't give much advice there. We watch when we really should be in bed. We both agree we watch too much. We have gone through streaks where we try to watch only every other night, which has helped in the past, but I guess we fell away from that. So maybe that's another method- only allow it on certain days. I bet your toddler can understand that. "I think we watch too much TV and we should be doing other more fun things! So from now on, we only watch TV on Tuesdays/Thursdays, and on MWF, I'll have another activity planned."
Another thought- a library is a nice place a 2-3 year old can stay busy and you can quietly nurse in a carrier.
Sorry this response isn't so well organized, but good luck! Report back, I'm curious to see how things go for you. I'll be trying on my end, too, to reduce TV in the evenings. We should use that 5-7 hours for something better for us- sleep, sex, creativity, productivity... so many other things. Also we have an ice cream habit that goes with the TV that should be dealt with...