This is a problem that Steam Family Share exists to solve.

Bro, seriously.

Your account is yours only. If you want to share your library with her, make her an account and add that to your famiy group. I do this with my 2 kids and everyone plays whatever they want, simultaneously.

Put your steam deck in offline mode, problem solved for anything that doesn’t need to ping a server. That’s what I do with my kids.

I don’t disagree on digital rights and all that, but I am able to game because of my Steam Deck.

Steam Families User Guide & FAQ: https://help.steampowered.com/en/faqs/view/054C-3167-DD7F-49D4

My understanding is this should fix your issue. Also, none of that is actually a Steam Deck issue.

Don't use the same account for 2 different people. Create another and use Steam Family sharing to fix your issue.

although you still won't "own" your games, but that's the life of a PC gamer. Best you can do is buy from GOG or find/run shady cracked versions.

Use Family Sharing, instead of sharing your account. Steam’s Family Sharing program is actually one of the most generous in the industry. It used to be the case where you’d get booted off of a game if the person who owned it opened a game. But they changed it a while back, to where you essentially have a digital bookshelf of games, and sharing members can choose from any game on the shelf. As long as you’re not trying to play the same game, everything is kosher. Or hell, you can even buy multiple copies of the same game if you want to play together, the same way you can keep multiple copies of a game on a shelf.

Switching accounts on the Steam Deck is easy too, because you simply pick which profile you want to use. You can set account restrictions, like maybe you only want your kid to be able to play E or E10+ ESRB rated games. Plus it means you’re not sharing save files, because each profile has their own saves; Anyone who has ever lost a cherished save file because of a younger sibling hitting “New Game” will be able to see the value in that. There’s very little reason to avoid setting up Family Sharing.

As many others have said, this is because you’re using the same account on both devices, and Steam’s DRM policies will stop you from being able to do what you described. So I won’t go into re-mentioning the many suggestions others have talked about.

What I do want to mention, however, is that this isn’t a problem that comes from having the Deck itself. Set up a separate computer in your living room and use your Steam account there, and you would have the same problem. Does that mean you should be turned off from buying a new computer that’ll run parallel to your main gaming rig?

Heroic Launcher and GOG is your friend. DRM free ftw.

But seriously Steam Family sharing is the way to go here.

They actually improved this recently however you need a second account and add it to your family, prior it would work just like this with one account, only one user can use a game attached to a library. However now as long as it's not the same game, it let's you play whatever on the second account.

I have set up a steam family and created accounts for my kids. Other than only having one copy of some games or games not supporting family sharing it's been great. I have control over the games they can see in their libraries and we can all play different or the same game with enough licenses at the same time. We often play valheim together.

Could your daughter play in offline mode? If it is not connected to the internet stream does not know you have two devices playing at a time.

im not giving my kid access to hentai puzzle castle 7.

How is this any different from not having a steam deck and having to share the one PC?

Nope. Stop sharing your steam account.

Just tested it to see what you’re talking about, I’ve never seen that before. Yeah that’s bullshit. It logs you out of the account (kind of?) and when you log back in, it logs out the other computer. What the hell.

I agree. While Family Sharing may be an option, it really shouldn't be necessary. Why shouldn't "I" (whether it's my dad playing Cities: Skylines, or actually me playing a round of Balatro on the Deck while waiting for a DotA queue to pop) be able to play two different games that I paid for at the same time without having to jump through any hoops? Before I knew about Family Sharing, I accidentally kicked my dad off Cities: Skylines far too many times simply by waking up my Deck.

Funnily enough, now Family Sharing largely isn't necessary because I started buying a bunch of my games on GOG which means I rarely use my Steam Deck because of how difficult most GOG games are to get running.

I agree that's not a good way for steam to handle it.
Seems to me that as long as it's on the same global IP address which indicate it's the same household, it should be considered OK.
But I do understand why they don't want to do what Netflix did originally, where people could share accounts without limit.