In marriages today, the husband and wife can decide to walk seperate ways for some reasons which they deem as non reconciliable. However the case maybe, skngle mothers are always welcome by God.
God never discriminate against anything he created which includes single mothers. The book of James advises believers to not hate or discriminate against each other for any reason.
James 2:1 f(KJV):
My brethren, have not the faith of our Lord Jesus Christ, the Lord of glory, with respect of persons.
God does not want anyone to perish and so he gave his only son to die for us so that we may be saved. He is a God that searcheth the heart and so as long as that single mother worship God in spirit and truth, then she is welcome to God.
2 Peter 3:9 (KJV):
The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
Remain Blessed !