If you move physically closer to the wireless network's host router will your devices connect faster and remain connected longer?
What make and model mini or micro USB wifi adapter are you using? How old?
The adapters may be able to receive wireless well but their ability to transmit is often weak. And in a busy wireless environment any responses that they send out may be lost in the electronic noise. Plus there may be additional interference from walls, appliances, and the general physical surroundings.
Sometimes a USB extension cable can be used to move and raise a wireless USB adapter up and away from the host device. Doing so may or may not help.
Also before using the android phone or tablet feel the adapter.
Then, after some usage or attempted usage, again (but carefully) feel the adapter. Is the adapter very warm or even hot? If so, that is a sign of a problem wireless USB adapter.
Overall though, if the problem is simply just an inability to connect to your home network then your devices are probably not correctly configured to do so.
Especially if you have made wireless connection/configuration changes in order to use public wireless networks. Or even wireless work networks.
Who has full admin rights to your home router and wireless network?
You will need help from that person to properly configure your Android phone and tablet to be allowed to connect to the home network.