How to limit screen time for different kids using the same iPad?

Sharing an AppleID between users is a bad idea.

Each child should have their own AppleID - in fact, every user should have their own AppleID. This is essential to maintain intended separation of activities and to avoid unintended sharing of unintended information and data.

You may find this information to be helpful with setting-up an AppleID for a minor - and in considering appropriate controls while continuing to share Apps and paid Apple services if you should choose to do so:

Apple for Kids - Official Apple Support

Help your child set up an iPhone, iPad, or iPod touch - Apple Support

Family Sharing and Apple ID for your child – Apple Support

Use parental controls on your child's iPhone, iPad and iPod touch – Apple Support

Outside of Educational and Enterprise establishments, iPad and iPhone are principally intended to be a single-user device used by one individual - and are not intended to shared in the same manner as you may be accustomed when using a Windows PC or Mac computer which can have multiple user profiles/accounts.

For managed environments, where multi-user usage is possible, the Deployment Guide provides appropriate guidance.

Shared iPad overview – Apple Support

For unmanaged environments, be aware that if you sign-out of iCloud and other Apple services - and allow another user to sign-in - you’ll not be able to change back for 90-days. So as to prevent account abuse, some critical Apple services will only allow one change of signed-in AppleID (on a device) in a 90-day period.

In conclusion, unless you fully understand and accept the implications, you would be well advised to reconsider any attempt to share your iPad with another user.

You're very welcome.

By far the simplest and most effective solution, without resorting to an Enterprise Management solution, is to simply have a dedicated iPad for each of your children (to be used with their own AppleID). They will each then be manageable using normal Parental Control and ScreenTime Restrictions as appropriate for each child. Each child will be able to maintain their own games, documents, preferences without risk of someone else changing, overwriting or deleting their own data (e.g. game progress).

If controlling an monitoring their activities, online or otherwise, you will have benefit of being able to easily separate the activities of each child.

Unfortunately, a third-party App cannot provide the level of control and/or flexibility that you are attempting to achieve.

If you intend to use your families devices interchangeably as you describe, you will need to employ a managed environment and an MDM solution (as used in Business/Enterprise/Educational deployments) to create and manage users and devices. This is likely to be considerably more administratively complex and financially expensive than you are perhaps likely to entertain.

If this is the direction that you wish to investigate, begin with reviewing these resources:

Intro to mobile device management profiles - Apple Support

Shared iPad overview – Apple Support