I have Broadcom BCM43142 802.11b/g/n too, and initially the laptop really really really doesn’t want to connect.
The modem makes it easy to create a 2nd connection, so I set the 1st (and best) as the primary option, whereas the 2nd as the alternative. It seems to toggle between them until it finally manages to connect and it stays connected.
No idea what do to make it run smoother.
Wired connections, whether through a USB 4g stick, or through Ethernet, works with no hiccups.
Sometimes I plug in a signal booster for the laptop, and when I use that to connect, it seems work as well, but it’s kind of a gamble because sometimes it works but at fairly slow speed.