Hi @Kat123h congratulations on your pregnancy! What you're suggesting is certainly possible although there's lots to think about when considering expressing routinely in the day for baby.
Firstly, I totally understand you not wanting to breastfeed in front of people. Lots of women feel this way, especially early on. There really are ways of feeding where noone can tell (the one top up one top down method) but if you weren't happy feeding in front of people you could always step out of the room perhaps?
It's worth looking into breastfeeding and how it works. Websites like NHS, Kelly mom, La Leche League and Association of Breastfeeding Mothers have lots of information. The main thing to understand is that it works on supply and demand. So your body will make enough milk for baby as long as baby (or a pump) is removing the milk from your breast.
If you're planning to bottle feed expressed milk when out, you would also need to be expressing around the same time to make up for that missed feed and maintain your supply. And honestly it is very hard to pump discretely (the pumps show your nipple being pulled into the flange although you can try a cover) and so at your in laws/ out and about you'd need to be doing that somewhere. So almost it would be easier to breastfeed in another room than pump. I always found pumping while out and about possible but can be a real faff and spilling milk and dealing with pump parts at other people's houses can be a bit awkward.
Ideally you could maybe start out breastfeeding so that you and baby get the hang of it then start pumping around 6 weeks. Also if you're going to combi feed you need to pace feed the bottle as this avoids bottle preference and feed responsively, not on a schedule. You also need to make sure everyone feeding baby will do the same.
I know you mentioned other people feeding baby. Often everyone wants to bond with baby and wants to do this by feeding. Feeding is not the only way for them to bond - skin to skin, baby wearing in a sling, changing nappies, bathing baby etc are all great and useful ways family and friends can bond. It's really important you have support and that people support you with breastfeeding and don't compete with it. It can be really hard sitting pumping milk (which lots of people don't enjoy) while someone else gets the enjoyment of feeding baby. But obviously if that's what you wanted then it's absolutely possible.
It may be worth giving the National Breastfeeding Helpline a call. They have volunteers who can answer lots of questions. Also, you'll probably have a local breastfeeding support group who can also help give information and support about all of this. They talk all things baby feeding not just direct breastfeeding.
Happy to answer any questions about pumping and storing milk too.