I have the absolute same baby but let me tell you what works for us. Ultimately Kali (my lil cutie pie) is very picky as to what she likes and doesnt like and like you i though I was gonna be home bound too but we have managed to reach compromises.
1st I SWEAR by the moby wrap Kali NEVER liked the baby sling not even as a fresh from the oven newborn so i went to mobywrap.com and looked at the instructions on how to wrap the fabric then I went to the fabric store and bought 6 1/2 yrds of cotton jersey and made one for myself (i got the measurements from another site). You just cut the fabric so its 22" wide by 6 1/2 yards long and get the wrapping instructions off the moby wrap website it is soooo much cheaper than buying the wrap. Kali will go ANYWHERE with me in that thing and is sleep most of the time while in it. But I wanted to get her used to the stroller because I fear with it becoming so hot she and I both may be miserable as the summer progresses.
So like most newborn strollers she sits in her carseat in the stroller until she's big enough to sit in the stroller seat alone and like Kelsey Kali screams bloody murder so this is what I've done. We went to babies r us and got this body insert for the carseat called a "snuzzler" and its made by a company called "kidepodemous" and you put it in the carseat so she's nice and snuggled from head to toe. I noticed that Kali hates the infant head rest that comes with the carseat b/c she can't turn her head the way she like. The snuzzler comes with a head rest too but its much more open and she seems to like it alot. How the snuzzler works is its padded up by the arms and sholders so she feels secure and I also have learned that she LOVES for me to ride over bumpy terrain she just drifts off to sleep.
We've been doing the stroller training for now 2 weeks and it is STILL very much a work in progress. I would suggest taking very, very short trips like to the end of the block and back home, I know its a pain believe me, but thats how we started. I'd sit her in the stroller and start pushing if she started crying I'd stop pick her up and comfort her til she calmed down then put her back in. We'd do this constantly until suddenly her crys changed from blood curdling to a bit whiny to finally none at all! Some other tips I would suggest are:
1) Keep the sun out her eyes (we use a sun hat and the carseat visor)
2) Make sure baby sees you at ALL times
3) Sing or talk constantly peeps look at me like I'm a fool because I carry on so bad but guess what it keeps her quiet!
4) have the moby wrap already tied around you while pushing the stroller so if worst come to worst you can just put her inside and walk home
5) Be patient :) it is absolutly something that takes time, my lil munchkin DOES NOT give in easily but we just go it a little at a time
Hope some of these suggestions help, sorry its so long, lol good luck and keep us posted!